Answers Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 3 A1 Glencoe Algebra 1 Lesson 3-1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME DATE PERIOD Chapter 3 5 Glencoe Algebra 1 Identify Linear Equations and Intercepts A linear equation is an equation that can be written in the form Ax + By = C. This is called the standard form of a linear equation. Determine whether y = 6 - 3x is a linear equation. Write the equation in standard form. First rewrite the equation so both variables are on the same side of the equation. y = 6 - 3x Original equation y + 3x = 6 - 3x + 3x Add 3x to each side. 3x + y = 6 Simplify. The equation is now in standard form, with A = 3, B = 1 and C = 6. This is a linear equation. Determine whether 3xy + y = 4 + 2x is a linear equation. Write the equation in standard form. Since the term 3xy has two variables, the equation cannot be written in the form Ax + By = C. Therefore, this is not a linear equation. Exercises Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. 1. 2x = 4y 2. 6 + y = 8 3. 4x - 2y = -1 4. 3xy + 8 = 4y 5. 3x - 4 = 12 6. y = x 2 + 7 7. y - 4x = 9 8. x + 8 = 0 9. -2x + 3 = 4y 10. 2 + 1 − 2 x = y 11. 1 − 4 y = 12 - 4x 12. 3xy - y = 8 13. 6x + 4y - 3 = 0 14. yx - 2 = 8 15. 6x - 2y = 8 + y 16. 1 − 4 x - 12y = 1 17. 3 + x + x 2 = 0 18. x 2 = 2xy Standard Form of a Linear Equation Ax + By = C, where A ≥ 0, A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1 Example 1 Example 2 3-1 Study Guide and Intervention Graphing Linear Equations yes; 2x - 4y = 0 yes; y = 2 yes; 4x - 2y = -1 no yes; 3x = 16 no yes; 4x - y = -9 yes; x = -8 yes; 2x + 4y = 3 yes; x - 2y = -4 yes; 16x + y = 48 no yes; 6x + 4y = 3 no yes; 6x - 3y = 8 yes; x - 48y = 4 no no Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME DATE PERIOD Chapter Resources Chapter 3 3 Glencoe Algebra 1 Before you begin Chapter 3 • Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS Statement STEP 2 A or D 1. The equation 6x + 2xy = 5 is a linear equation because each variable is to the first power. 2. The graph of y = 0 has more than one x-intercept. 3. The zero of a function is located at the y-intercept of the function. 4. All horizontal lines have an undefined slope. 5. The slope of a line can be found from any two points on the line. 6. A direct variation, y = kx, will always pass through the origin. 7. In a direct variation y = kx, if k < 0 then its graph will slope upward from left to right. 8. A sequence is arithmetic if the difference between all consecutive terms is the same. 9. Each number in a sequence is called a factor of that sequence. 10. Making a conclusion based on a pattern of examples is called inductive reasoning. After you complete Chapter 3 • Reread each statement and complete the last column by entering an A or a D. • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a piece of paper to write an example of why you disagree. Step 1 Step 2 3 Anticipation Guide Linear Functions D A D D A A D A D A Answers (Anticipation Guide and Lesson 3-1)
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Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A1 Glencoe Algebra 1
Lesson 3-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
5
Gle
nc
oe
Alg
eb
ra 1
Ide
nti
fy L
ine
ar
Eq
ua
tio
ns
an
d I
nte
rce
pts
A
lin
ea
r e
qu
ati
on
is
an
equ
ati
on
th
at
can
be w
ritt
en
in
th
e f
orm
Ax
+ B
y =
C. T
his
is
call
ed
th
e s
tan
da
rd
fo
rm
of
a l
inear
equ
ati
on
.
D
ete
rm
ine
wh
eth
er y
= 6
- 3
x
is a
lin
ea
r e
qu
ati
on
. W
rit
e t
he
eq
ua
tio
n i
n
sta
nd
ard
fo
rm
.
Fir
st r
ew
rite
th
e e
qu
ati
on
so b
oth
vari
able
s are
on
th
e s
am
e s
ide o
f th
e e
qu
ati
on
.
y =
6 -
3x
Ori
gin
al equation
y +
3x =
6 -
3x +
3x
Add 3
x t
o e
ach s
ide.
3x +
y =
6
Sim
plif
y.
Th
e e
qu
ati
on
is
now
in
sta
nd
ard
form
, w
ith
A =
3,
B =
1 a
nd
C =
6. T
his
is
a l
inear
equ
ati
on
.
D
ete
rm
ine
wh
eth
er 3
xy +
y =
4 +
2x
is a
lin
ea
r e
qu
ati
on
. W
rit
e t
he
eq
ua
tio
n i
n s
tan
da
rd
fo
rm
.
Sin
ce t
he t
erm
3xy h
as
two v
ari
able
s,
the e
qu
ati
on
can
not
be w
ritt
en
in
th
e
form
Ax +
By =
C. T
here
fore
, th
is i
s n
ot
a l
inear
equ
ati
on
.
Exerc
ises
De
term
ine
wh
eth
er e
ach
eq
ua
tio
n i
s a
lin
ea
r e
qu
ati
on
. W
rit
e y
es o
r n
o.
If y
es,
writ
e t
he
eq
ua
tio
n i
n s
tan
da
rd
fo
rm
.
1. 2
x =
4y
2. 6 +
y =
8
3. 4x
- 2
y =
-1
4. 3xy
+ 8
= 4
y
5. 3x
- 4
= 1
2
6. y
= x
2 +
7
7. y
- 4
x =
9
8. x
+ 8
= 0
9.
-2x
+ 3
= 4
y
10. 2
+ 1
−
2 x
= y
11. 1
−
4 y
= 1
2 -
4x
12. 3
xy
- y
= 8
13. 6x
+ 4
y -
3 =
0
14. yx
- 2
= 8
15. 6x
- 2
y =
8 +
y
16. 1
−
4 x
- 1
2y
= 1
17. 3
+ x
+ x
2 =
0
18. x
2 =
2xy
Sta
nd
ard
Fo
rm o
f a
Lin
ea
r E
qu
ati
on
Ax +
By
= C
, w
he
re A
≥ 0
, A
an
d B
are
no
t b
oth
ze
ro,
an
d A
, B
, a
nd
C a
re in
teg
ers
with
a g
rea
test
co
mm
on
fa
cto
r o
f 1
Exam
ple
1Exam
ple
2
3-1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Gra
ph
ing
Lin
ear
Eq
uati
on
s
y
es;
2x
- 4
y =
0
yes;
y =
2
yes;
4x
- 2
y =
-1
n
o
yes;
3x
= 1
6
no
y
es;
4x
- y
= -
9
yes;
x =
-8
yes;
2x
+ 4
y =
3
y
es;
x -
2y
= -
4
yes;
16x
+ y
= 4
8
no
y
es;
6x
+ 4
y =
3
no
y
es;
6x
- 3
y =
8
y
es;
x -
48
y =
4
no
n
o
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Chapter Resources
Ch
ap
ter
3
3
Gle
nc
oe
Alg
eb
ra 1
B
efo
re y
ou
beg
in C
ha
pte
r 3
•
R
ead
each
sta
tem
en
t.
•
D
eci
de w
heth
er
you
Agre
e (
A)
or
Dis
agre
e (
D)
wit
h t
he s
tate
men
t.
•
W
rite
A o
r D
in
th
e f
irst
colu
mn
OR
if
you
are
not
sure
wh
eth
er
you
agre
e o
r d
isagre
e, w
rite
NS
(N
ot
Su
re).
ST
EP
1A
, D
, o
r N
SS
tate
men
tS
TE
P 2
A o
r D
1
. T
he e
qu
ati
on
6x +
2xy =
5 i
s a l
inear
equ
ati
on
beca
use
each
vari
able
is
to t
he f
irst
pow
er.
2
. T
he g
rap
h o
f y =
0 h
as
more
th
an
on
e x
-in
terc
ep
t.
3
. T
he z
ero
of
a f
un
ctio
n i
s lo
cate
d a
t th
e y
-in
terc
ep
t of
the
fun
ctio
n.
4
. A
ll h
ori
zon
tal
lin
es
have a
n u
nd
efi
ned
slo
pe.
5
. T
he s
lop
e o
f a l
ine c
an
be f
ou
nd
fro
m a
ny t
wo p
oin
ts o
n t
he
lin
e.
6
. A
dir
ect
vari
ati
on
, y =
kx, w
ill
alw
ays
pass
th
rou
gh
th
e o
rigin
.
7
. In
a d
irect
vari
ati
on
y =
kx, if
k <
0 t
hen
its
gra
ph
wil
l sl
op
e
up
ward
fro
m l
eft
to r
igh
t.
8
. A
sequ
en
ce i
s ari
thm
eti
c if
th
e d
iffe
ren
ce b
etw
een
all
co
nse
cuti
ve t
erm
s is
th
e s
am
e.
9
. E
ach
nu
mber
in a
sequ
en
ce i
s ca
lled
a f
act
or
of
that
sequ
en
ce.
10
. M
ak
ing a
con
clu
sion
base
d o
n a
patt
ern
of
exam
ple
s is
call
ed
in
du
ctiv
e r
easo
nin
g.
A
fter y
ou
co
mp
lete
Ch
ap
ter 3
•
R
ere
ad
each
sta
tem
en
t an
d c
om
ple
te t
he l
ast
colu
mn
by e
nte
rin
g a
n A
or
a D
.
•
D
id a
ny o
f you
r op
inio
ns
abou
t th
e s
tate
men
ts c
han
ge f
rom
th
e f
irst
colu
mn
?
•
F
or
those
sta
tem
en
ts t
hat
you
mark
wit
h a
D, u
se a
pie
ce o
f p
ap
er
to w
rite
an
exam
ple
of
wh
y y
ou
dis
agre
e.
Ste
p 1
Ste
p 2
3A
nti
cip
ati
on
Gu
ide
Lin
ear
Fu
ncti
on
s
D A D D A A D A D A
Answers (Anticipation Guide and Lesson 3-1)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A2 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
6
Gle
nc
oe
Alg
eb
ra 1
Gra
ph
Lin
ear
Eq
uati
on
s T
he g
rap
h o
f a l
inear
equ
ati
on
s re
pre
sen
ts a
ll t
he s
olu
tion
s of
the e
qu
ati
on
. A
n x
-coord
inate
of
the p
oin
t at
wh
ich
a g
rap
h o
f an
equ
ati
on
cro
sses
the x
-axis
in
an
x-i
nte
rcep
t. A
y-c
oord
inate
of
the p
oin
t at
wh
ich
a g
rap
h c
ross
es
the y
-axis
is
call
ed
a
y-i
nte
rce
pt.
G
ra
ph
3x
+ 2y
= 6
by
usin
g t
he
x-
an
d y
-in
terce
pts
.
To f
ind
th
e x
-in
terc
ep
t, l
et
y =
0 a
nd
so
lve f
or
x. T
he x
-in
terc
ep
t is
2. T
he
gra
ph
in
ters
ect
s th
e x
-axis
at
(2, 0).
To f
ind
th
e y
-in
terc
ep
t, l
et
x =
0 a
nd
so
lve f
or
y.
Th
e y
-in
terc
ep
t is
3. T
he g
rap
h
inte
rsect
s th
e y
-axis
at
(0, 3).
Plo
t th
e p
oin
ts (
2, 0)
an
d (
0, 3)
an
d
dra
w t
he l
ine t
hro
ugh
th
em
.
Exerc
ises
Gra
ph
ea
ch
eq
ua
tio
n b
y u
sin
g t
he
x-
an
d y
-in
terce
pts
.
1. 2
x +
y =
-2
2. 3
x -
6y
= -
3
3.
-2x
+ y
= -
2
x
y
Ox
y Ox
y O
Gra
ph
ea
ch
eq
ua
tio
n b
y m
ak
ing
a t
ab
le.
4. y
= 2
x
5. x
- y
= -
1
6. x
+ 2
y =
4
x
y
Ox
y
Ox
y O
x
y O
G
ra
ph
y -
2x
= 1
by
ma
kin
g
a t
ab
le.
Solv
e t
he e
qu
ati
on
for
y.
y
- 2
x =
1
Ori
gin
al equation
y -
2x
+ 2
x =
1 +
2x
Add 2
x t
o e
ach s
ide.
y
= 2
x +
1
Sim
plif
y.
Sele
ct f
ive v
alu
es
for
the d
om
ain
an
d m
ak
e a
table
. T
hen
gra
ph
th
e o
rdere
d p
air
s an
d d
raw
a l
ine
thro
ugh
th
e p
oin
ts.
y
xO
( 2, 0
)
( 0, 3
)
x2
x +
1y
(x, y)
-2
2(-
2)
+ 1
-3
(-2
, -
3)
-1
2(-
1)
+ 1
-1
(-1
, -
1)
0
2(0
) +
1
1(0
, 1
)
1
2(1
) +
1
3(1
, 3
)
2
2(2
) +
1 5
(2,
5)
Exam
ple
1Exam
ple
2
3-1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
(con
tin
ued
)
Gra
ph
ing
Lin
ear
Eq
uati
on
s
Lesson 3-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
7
Gle
nc
oe
Alg
eb
ra 1
De
term
ine
wh
eth
er e
ach
eq
ua
tio
n i
s a
lin
ea
r e
qu
ati
on
. W
rit
e yes o
r no
.
If y
es,
writ
e t
he
eq
ua
tio
n i
n s
tan
da
rd
fo
rm
.
1. xy
= 6
2. y
= 2
- 3
x
3. 5x
= y
- 4
4. y
= 2
x +
5
5. y
= -
7 +
6x
6. y
= 3
x2 +
1
7. y
- 4
= 0
8. 5x
+ 6
y =
3x
+ 2
9. 1
−
2 y
= 1
Fin
d t
he
x-
an
d y
-in
terce
pts
of
ea
ch
lin
ea
r f
un
cti
on
.
10.
11.
12.
Gra
ph
ea
ch
eq
ua
tio
n b
y m
ak
ing
a t
ab
le.
13. y
= 4
14. y
= 3
x
15. y
= x
+ 4
Gra
ph
ea
ch
eq
ua
tio
n b
y u
sin
g t
he
x-
an
d y
-in
terce
pts
.
16. x
- y
= 3
17. 10x
= -
5y
18. 4x
= 2
y +
6
x
y
O
x
y
Ox
y
O
x
y
Ox
y
Ox
y
O
x
y
Ox
y
Ox
y
O
3-1
Sk
ills
Pra
ctic
e
Gra
ph
ing
Lin
ear
Eq
uati
on
s
n
o
yes;
3x
+ y
= 2
y
es;
5x
- y
= -
4
y
es;
2x
- y
= -
5
yes;
6x
- y
= 7
n
o
y
es;
y =
4
yes;
x +
3y
= 1
y
es;
y =
2
x
-in
terc
ep
t: 2
,
x-i
nte
rcep
t: 4
, x
-in
terc
ep
t: 2
,
y-i
nte
rcep
t: -
2
y-i
nte
rcep
t: 4
y
-in
terc
ep
t: 4
Answers (Lesson 3-1)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A3 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
8
Gle
nc
oe
Alg
eb
ra 1
De
term
ine
wh
eth
er e
ach
eq
ua
tio
n i
s a
lin
ea
r e
qu
ati
on
. W
rit
e yes o
r no
. If
ye
s,
writ
e t
he
eq
ua
tio
n i
n s
tan
da
rd
fo
rm
an
d d
ete
rm
ine
th
e x-
an
d y-i
nte
rce
pts
.
1. 4xy
+ 2
y =
9
2. 8
x -
3y
= 6
- 4
x
3. 7x
+ y
+ 3
= y
4. 5
- 2
y =
3x
5.
x
−
4 -
y
−
3 =
1
6. 5
−
x -
2
−
y =
7
Gra
ph
ea
ch
eq
ua
tio
n.
7. 1
−
2 x
- y
= 2
8. 5x
- 2
y =
7
9. 1.5
x +
3y
= 9
10
. CO
MM
UN
ICA
TIO
NS
A t
elep
hon
e co
mp
an
y c
harg
es
$4.9
5 p
er m
onth
for
lon
g d
ista
nce
call
s p
lus
$0.0
5 p
er
min
ute
. T
he
mon
thly
cos
t c
of l
ong d
ista
nce
call
s ca
n b
e d
escr
ibed
by t
he
equ
ati
on c
= 0
.05
m +
4.9
5, w
her
e m
is
the
nu
mber
of
min
ute
s.
a.
Fin
d t
he
y-i
nte
rcep
t of
th
e gra
ph
of
the
equ
ati
on.
b.
Gra
ph
th
e eq
uati
on.
c.
If y
ou t
alk
140 m
inu
tes,
wh
at
is t
he
mon
thly
cos
t?
11
. MA
RIN
E B
IOLO
GY
K
ille
r w
hale
s u
suall
y s
wim
at
a
rate
of
3.2
–9.7
kil
omet
ers
per
hou
r, t
hou
gh
th
ey c
an
tra
vel
u
p t
o 48.4
kil
omet
ers
per
hou
r. S
up
pos
e a m
igra
tin
g k
ille
r w
hale
is
swim
min
g a
t an
aver
age
rate
of
4.5
kil
omet
ers
per
h
our.
Th
e d
ista
nce
d t
he
wh
ale
has
travel
ed i
n t
hou
rs c
an
be
pre
dic
ted
by t
he
equ
ati
on d
= 4
.5t.
a.
Gra
ph
th
e eq
uati
on.
b.
Use
th
e gra
ph
to
pre
dic
t th
e ti
me
it t
ak
es t
he
kil
ler
wh
ale
to
travel
30 k
ilom
eter
s.
Tim
e (
ho
urs
)
Kil
ler
Wh
ale
Tra
vels
Distance (km)
02
46
89
13
57
40
35
30
25
20
15
10 5
Tim
e (
min
ute
s)
Lo
ng
Dis
tan
ce
Cost ($)
040
80
120
160
14
12
10 8 6 4 2
x
y
O
x
y
Ox
y
O
3-1
Practi
ce
Gra
ph
ing
Lin
ear
Eq
uati
on
s
n
o
yes;
4x
- y
= 2
; y
es;
7x
= -
3;
x:
1
−
2 ;
y:
-2
x:
-3
−
7 ;
y:
no
ne
y
es;
3x
+ 2
y =
5;
yes;
3x
- 4
y =
12;
n
o
x
: 5
−
3 ; y
: 5
−
2
x:
4;
y:
-3
(0, 4.9
5)
$11
.95
betw
een
6 h
an
d 7
h
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 3-1
Ch
ap
ter
3
9
Gle
nc
oe
Alg
eb
ra 1
1.FO
OT
BA
LL
On
e fo
otball
sea
son
, th
e C
aro
lin
a P
an
ther
s w
on 4
mor
e gam
es
than
th
ey l
ost.
Th
is c
an
be
rep
rese
nte
d
by y
= x
+ 4
, w
her
e x i
s th
e n
um
ber
of
gam
es l
ost
an
d y
is
the
nu
mber
of
gam
es
won
. W
rite
th
is l
inea
r eq
uati
on i
n
stan
dard
for
m.
2. T
OW
ING
Pic
k-M
-Up
Tow
ing C
omp
an
y
charg
es $
40 t
o h
ook
a c
ar
an
d $
1.7
0 f
or
each
mil
e th
at
it i
s to
wed
. T
he
equ
ati
on
y =
1.7
x +
40 r
epre
sen
ts t
he
tota
l co
st y
fo
r x m
iles
tow
ed. D
eter
min
e th
e y-i
nte
rcep
t. D
escr
ibe
wh
at
the
valu
e m
ean
s in
th
is c
onte
xt.
3. S
HIP
PIN
G T
he
OO
CL
Sh
enzh
en,
one
of
the
wor
ld’s
larg
est
con
tain
er s
hip
s,
carr
ies
8063 T
EU
s (1
280 c
ubic
fee
t co
nta
iner
s). W
ork
ers
can
un
load
a s
hip
at
a r
ate
of
a T
EU
ever
y m
inu
te. U
sin
g
this
rate
, w
rite
an
d g
rap
h a
n e
qu
ati
on t
o d
eter
min
e h
ow m
an
y h
ours
it
wil
l ta
ke
the
wor
ker
s to
un
load
half
of
the
con
tain
ers
from
th
e S
hen
zhen
.
4. B
US
INE
SS
Th
e eq
uati
on
y =
1000
x -
5000 r
epre
sen
ts t
he
mon
thly
pro
fits
of
a s
tart
-up
dry
cl
ean
ing c
omp
an
y. T
ime
in m
onth
s is
x a
nd
pro
fit
in d
olla
rs i
s y. T
he
firs
t d
ate
of
oper
ati
on i
s w
hen
tim
e is
zer
o.
How
ever
, p
rep
ara
tion
for
op
enin
g t
he
bu
sin
ess
beg
an
3 m
onth
s ea
rlie
r w
ith
th
e p
urc
hase
of
equ
ipm
ent
an
d s
up
pli
es.
Gra
ph
th
e li
nea
r fu
nct
ion
for
x-v
alu
es
from
-3 t
o 8.
5. B
ON
E G
RO
WT
H
Th
e h
eigh
t of
a
wom
an
can
be
pre
dic
ted
by t
he
equ
ati
on
h =
81.2
+ 3
.34r,
wh
ere
h i
s h
er h
eigh
t in
ce
nti
met
ers
an
d r
is
the
len
gth
of
her
ra
diu
s bon
e in
cen
tim
eter
s.
a.
Is t
his
is
a l
inea
r fu
nct
ion
? E
xp
lain
.
b.
Wh
at
are
th
e r-
an
d h
-in
terc
epts
of
the
equ
ati
on?
Do
they
mak
e se
nse
in
th
e si
tuati
on?
Exp
lain
.
c.
Use
th
e fu
nct
ion
to
fin
d t
he
ap
pro
xim
ate
hei
gh
t of
a w
oman
wh
ose
rad
ius
bon
e is
25 c
enti
met
ers
lon
g.
y
x2
46
8
O
2000
-2000
-4000
-6000
-8000
Tim
e (
ho
urs
)
20
10
040
30
y
x50
60
70
80
TEUs on Ship (thousands)
34 2 1589 7 6
3-1
Wo
rd
Pro
ble
m P
racti
ce
Gra
ph
ing
Lin
ear
Eq
uati
on
s
x -
y =
-4
T
he y
-in
terc
ep
t is
40, w
hic
h i
s t
he
fee t
o h
oo
k t
he c
ar.
y
= 8
063
- 6
0x;
ab
ou
t 67.
4 h
ou
rs,
or
67 h
ou
rs a
nd
21.
5 m
inu
tes
yes;
the e
qu
ati
on
can
be w
ritt
en
in
sta
nd
ard
fo
r w
here
A =
1,
B =
-3.3
4, an
d C
= -
81.
2.
y-i
nte
rcep
t =
81.
2;
x-i
nte
rcep
t ≈
-
24.3
; n
o, w
e w
ou
ld e
xp
ect
a
wo
man
81.
2 c
m t
all t
o h
ave a
rms,
an
d a
neg
ati
ve r
ad
ius l
en
gth
has
no
real
mean
ing
.
165 c
m
Answers (Lesson 3-1)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A4 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
10
G
len
co
e A
lge
bra
1
Tran
sla
tin
g L
inear
Gra
ph
s
Lin
ear
gra
ph
s ca
n b
e tr
an
sla
ted
on
th
e co
ord
inate
pla
ne.
Th
is m
ean
s th
at
the
gra
ph
mov
es
up, d
own
, ri
gh
t, o
r le
ft w
ith
out
chan
gin
g i
ts d
irec
tion
.
Tra
nsl
ati
ng t
he
gra
ph
s u
p o
r d
own
aff
ects
th
e y-c
oord
inate
for
a g
iven
x v
alu
e. T
ran
slati
ng
the
gra
ph
rig
ht
or l
eft
aff
ects
th
e x-c
oord
inate
for
a g
iven
y-v
alu
e.
T
ra
nsl
ate
th
e g
ra
ph
of y =
2x
+ 2
, 3
un
its
up
.
Exerc
ises
Gra
ph
th
e f
un
cti
on
an
d t
he
tra
nsl
ati
on
on
th
e s
am
e c
oo
rd
ina
te p
lan
e.
1. y
= x
+ 4
, 3 u
nit
s d
own
2. y
= 2
x –
2, 2
un
its
left
3. y
= -
2x
+ 1
, 1
un
it r
igh
t 4. y
= -
x -
3, 2
un
its
up
Ad
d 3
to
ea
ch
y-v
alu
e.
y
xO
y =
2x +
2
y
xO
y =
x +
4
y
xO
y =
2x -
2
y
xO
y =
-2
x +
1
y
xO
y =
-x -
3
y =
2x +
2
xy
-1
0
02
14
26
Tra
nsla
tio
n
xy
-1
3
05
17
29
Exam
ple
3-1
En
rich
men
t
Lesson 3-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
11
G
len
co
e A
lge
bra
1
In a
dd
itio
n t
o or
gan
izin
g d
ata
, a s
pre
ad
shee
t ca
n b
e u
sed
to
rep
rese
nt
data
gra
ph
icall
y.
Exerc
ises
1. A
ph
oto
pri
nte
r of
fers
a s
ubsc
rip
tion
for
dig
ital
ph
oto
fin
ish
ing. T
he
subsc
rip
tion
cos
ts
$4.9
9 p
er m
onth
. E
ach
sta
nd
ard
siz
e p
hot
o a s
ubsc
riber
pri
nts
cos
ts $
0.1
9. U
se a
sp
read
shee
t to
gra
ph
th
e eq
uati
on y
= 4
.99
+ 0
.19x, w
her
e x i
s th
e n
um
ber
of
ph
otos
p
rin
ted
an
d y
is
the
tota
l m
onth
ly c
ost.
2. A
lon
g d
ista
nce
ser
vic
e p
lan
in
clu
des
a $
8.9
5 p
er m
onth
fee
plu
s $0.0
5 p
er m
inu
te o
f ca
lls.
Use
a s
pre
ad
shee
t to
gra
ph
th
e eq
uati
on y
= 8
.95
+ 0
.05
x, w
her
e x i
s th
e n
um
ber
of
min
ute
s of
call
s an
d y
is
the
tota
l m
onth
ly c
ost.
A
n i
nte
rn
et
re
tail
er c
ha
rg
es
$1
.99
pe
r o
rd
er p
lus
$0
.99
pe
r i
tem
to
sh
ip b
oo
ks
an
d C
Ds.
Gra
ph
th
e e
qu
ati
on
y =
1.9
9 +
0.9
9x,
wh
ere
x i
s th
e n
um
be
r o
f it
em
s o
rd
ere
d a
nd
y i
s th
e s
hip
pin
g c
ost
.
Ste
p 1
U
se c
olu
mn
A f
or t
he
nu
mber
s of
ite
ms
an
d
colu
mn
B f
or t
he
ship
pin
g c
osts
.
Ste
p 2
C
reate
a g
rap
h f
rom
th
e d
ata
. S
elec
t th
e d
ata
in
col
um
ns
A a
nd
B a
nd
sel
ect
Ch
art
fro
m t
he
Inse
rt m
enu
. S
elec
t an
XY
(S
catt
er)
chart
to
show
th
e d
ata
poi
nts
con
nec
ted
wit
h l
ine
segm
ents
.
A1 4 5 6 7 8 9 10
11
122 3
B
Sh
ipp
ing
.xls
Ite
ms
Sh
ipp
ing
Co
st
1 2 3 4 5 6 7 8 9
10
$2
.98
$3
.97
$4
.96
$5
.95
$6
.94
$7
.93
$8
.92
$9
.91
$1
0.9
0
$1
1.8
9
Sh
eet
1S
heet
2S
heet
Exam
ple
3-1
Sp
read
sheet
Act
ivit
y
Lin
ear
Eq
uati
on
s
See s
tud
en
ts’ w
ork
.
See s
tud
en
ts’ w
ork
.
Answers (Lesson 3-1)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A5 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
12
G
len
co
e A
lge
bra
1
So
lve
by
Gra
ph
ing
Y
ou c
an
sol
ve
an
equ
ati
on b
y g
rap
hin
g t
he
rela
ted
fu
nct
ion
. T
he
solu
tion
of
the
equ
ati
on i
s th
e x-i
nte
rcep
t of
th
e fu
nct
ion
.
S
olv
e t
he
eq
ua
tio
n 2x -
2 =
-4
by
gra
ph
ing
.
Fir
st s
et t
he
equ
ati
on e
qu
al
to 0
. T
hen
rep
lace
0 w
ith
f(x
). M
ak
e a t
able
of
ord
ered
pair
so
luti
ons.
Gra
ph
th
e fu
nct
ion
an
d l
ocate
th
e x-i
nte
rcep
t.
2x -
2 =
-4
2x -
2 +
4 =
-4 +
4
2
x +
2 =
0
f(x
) =
2x +
2
To
gra
ph
th
e fu
nct
ion
, m
ak
e a t
able
. G
rap
h t
he
ord
ered
pair
s.
x
f(x)
= 2
x +
2f(
x)
[x, f(
x)]
1f(
1)
= 2
(1)
+ 2
4(1
, 4
)
-1
f(-
1)
= 2
(-1
) +
20
(-1
, 0
)
-2
f(-
2)
= 2
(-2
) +
2
-2
(-2
, -
2)
y
x
Th
e gra
ph
in
ters
ects
th
e x-a
xis
at
(-1, 0).
Th
e so
luti
on t
o th
e eq
uati
on i
s x =
-1.
Exerc
ises
So
lve
ea
ch
eq
ua
tio
n.
1
. 3
x -
3 =
0 1
2
. -
2x +
1 =
5 -
2x
3.
-x +
4 =
0 4
y
xO
y
xO
y
xO
4
. 0 =
4x -
1
1
−
4
5. 5x -
1 =
5x
6.
-3x +
1 =
0
1
−
3
y
x
y
xO
y
xO
Ori
gin
al equation
Add 4
to e
ach s
ide.
Sim
plif
y.
Repla
ce 0
with f
(x).
Exam
ple
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
So
lvin
g L
inear
Eq
uati
on
s b
y G
rap
hin
g
3-2
Lesson 3-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
13
G
len
co
e A
lge
bra
1
Est
ima
te S
olu
tio
ns
by
Gra
ph
ing
S
omet
imes
gra
ph
ing d
oes
not
pro
vid
e an
exact
so
luti
on, bu
t on
ly a
n e
stim
ate
. In
th
ese
case
s, s
olve
alg
ebra
icall
y t
o fi
nd
th
e ex
act
sol
uti
on.
WA
LK
ING
Y
ou
an
d y
ou
r c
ou
sin
de
cid
e t
o w
alk
th
e 7
-mil
e t
ra
il a
t
the
sta
te p
ark
to
th
e r
an
ge
r s
tati
on
. T
he
fu
ncti
on
d =
7 –
3.2t r
ep
re
se
nts
yo
ur
dis
tan
ce
d f
ro
m t
he
ra
ng
er s
tati
on
aft
er t
ho
urs.
Fin
d t
he
ze
ro
of
this
fu
ncti
on
.
De
scrib
e w
ha
t th
is v
alu
e m
ea
ns i
n t
his
co
nte
xt.
Mak
e a t
able
of
valu
es t
o gra
ph
th
e fu
nct
ion
.
t
d =
7 -
3.2
td
(t, d
)
0d
= 7
- 3
.2(0
) 7
(0
, 7
)
1d
= 7
- 3
.2(1
)3
.8(1
, 3
.8)
2d
= 7
- 3
.2(2
)0
.6(2
, 0
.6)
Miles from Ranger Station
23 1
0
45678y
Tim
e (h
ou
rs)
21
x3
Th
e gra
ph
in
ters
ects
th
e t–
axis
bet
wee
n t
= 2
an
d t
= 3
, bu
t cl
oser
to
t =
2. It
wil
l ta
ke
you
an
d y
our
cou
sin
ju
st
over
tw
o h
ours
to
reach
th
e ra
nger
sta
tion
.
You
can
ch
eck
you
r es
tim
ate
by s
olvin
g t
he
equ
ati
on a
lgeb
raic
all
y.
Exerc
ises
1
. M
US
IC Jes
sica
wan
ts t
o re
cord
her
favor
ite
son
gs
to
one
CD
. T
he
fun
ctio
n C
= 8
0 -
3.2
2n
rep
rese
nts
th
e re
cord
ing
tim
e C
avail
able
aft
er n
son
gs
are
rec
ord
ed. F
ind
th
e ze
ro o
f th
is f
un
ctio
n. D
escr
ibe
wh
at
this
valu
e m
ean
s in
th
is c
onte
xt.
ju
st
un
der
25;
on
ly 2
4 s
on
gs c
an
be r
eco
rded
on
on
e C
D
2
. G
IFT
CA
RD
S E
nri
qu
e u
ses
a g
ift
card
to
bu
y c
offe
e at
a
coff
ee s
hop
. T
he
init
ial
valu
e of
th
e gif
t ca
rd i
s $20. T
he
fun
ctio
n n
= 2
0 –
2.7
5c
rep
rese
nts
th
e am
oun
t of
mon
ey s
till
le
ft o
n t
he
gif
t ca
rd n
aft
er p
urc
hasi
ng c
cu
ps
of c
offe
e. F
ind
th
e ze
ro o
f th
is f
un
ctio
n. D
escr
ibe
wh
at
this
valu
e m
ean
s in
th
is c
onte
xt.
ju
st
over
7;
En
riq
ue c
an
bu
y 7
cu
ps o
f co
ffee
wit
h t
he g
ift
card
Time Available (min)
10 0
20
30
40
50
60
70
80
90
Nu
mb
er o
f So
ngs
51
01
52
02
53
0
Exam
ple
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
So
lvin
g L
inear
Eq
uati
on
s b
y G
rap
hin
g
3-2
Value Left on Card ($)
4 08
12
16
20
24
Co
ffee
s B
ou
ght
24
68
10
12
Answers (Lesson 3-2)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A6 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
14
G
len
co
e A
lge
bra
1
So
lve
ea
ch
eq
ua
tio
n.
1
. 2
x -
5 =
-3 +
2x
2.
-3x +
2 =
0
3. 3x +
2 =
3x -
1
y
x
y
x
y
x
4
. 4
x -
1 =
4x +
2
5. 4x -
1 =
0
6. 0 =
5x +
3
y
x
y
x
y
x
7
. 0 =
-2
x +
4
8.
-3x +
8 =
5 -
3x
9.
-x +
1 =
0
y
x
y
x
y
x
10
. G
IFT
CA
RD
S Y
ou
rece
ive a
gif
t ca
rd f
or
trad
ing c
ard
s fr
om
a l
oca
l st
ore
. T
he f
un
ctio
n
d =
20 -
1.9
5c r
ep
rese
nts
th
e r
em
ain
ing d
oll
ars
d o
n t
he g
ift
card
aft
er
obta
inin
g c
pack
ages
of
card
s. F
ind
th
e z
ero
of
this
fu
nct
ion
. D
esc
ribe
wh
at
this
valu
e m
ean
s in
th
is c
on
text.
≈
10.2
6;
yo
u c
an
pu
rch
ase 1
0 p
ackag
es
of
trad
ing
card
s w
ith
th
e g
ift
card
.
Amount Remaining on Gift Card ($)
2 0468
10
12
14
16
18
20d
Pac
kage
s o
f C
ard
s B
ou
ght
12
34
56
78
91
0c
d =
20 -
1.9
5c
no
so
luti
on
2
−
3
no
so
luti
on
no
so
luti
on
1
−
4
- 3
−
5
no
so
luti
on
21
Sk
ills
Practi
ce
So
lvin
g L
inear
Eq
uati
on
s b
y G
rap
hin
g
3-2
Lesson 3-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
15
G
len
co
e A
lge
bra
1
Practi
ce
So
lvin
g L
inear
Eq
uati
on
s b
y G
rap
hin
g
So
lve
ea
ch
eq
ua
tio
n.
1
. 1
−
2 x
- 2
= 0
4
2.
-3x +
2 =
-1
1
3. 4x -
2 =
-2
0
y
xO
O
y
x
y
x
4
. 1
−
3 x
+ 2
= 1
−
3 x
- 1
5
. 2
−
3 x
+ 4
= 3
6
. 3
−
4 x
+ 1
= 3
−
4 x
- 7
n
o s
olu
tio
n
- 3
−
2
no
so
luti
on
y
x
y
x
y
x
So
lve
ea
ch
eq
ua
tio
n b
y g
ra
ph
ing
. V
erif
y y
ou
r a
nsw
er a
lge
bra
ica
lly
7
. 13
x +
2 =
11x -
1
8.
-9x -
3 =
-4
x -
3
9.
- 1
−
3 x
+ 2
= 2
−
3 x
- 1
- 3
−
2
0
3
y
x
y
x
y
x
10
. D
ISTA
NC
E A
bu
s is
dri
vin
g a
t 60 m
iles
per
hou
r
tow
ard
a b
us
stati
on
th
at
is 2
50 m
iles
aw
ay.
Th
e
fun
ctio
n d
= 2
50 –
60t
rep
rese
nts
th
e d
ista
nce
d f
rom
the b
us
stati
on
th
e b
us
is t
hou
rs a
fter
it h
as
start
ed
dri
vin
g. F
ind
th
e z
ero
of
this
fu
nct
ion
. D
esc
ribe w
hat
this
valu
e m
ean
s in
th
is c
on
text.
Distance from BusStation (miles)
50 0
10
0
15
0
20
0
25
0
30
0
Tim
e (h
ou
rs)
12
34
56
3-2 ≈
4.1
7 h
r; t
he b
us w
ill
ari
ve a
t th
e s
tati
on
in
ap
pro
xim
ate
ly 4
.17 h
ou
rs.
Answers (Lesson 3-2)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A7 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
16
G
len
co
e A
lge
bra
1
Wo
rd
Pro
ble
m P
racti
ce
So
lvin
g L
inear
Eq
uati
on
s b
y G
rap
hin
g
1
. P
ET
CA
RE
You
bu
y a
6.3
-pou
nd
bag
of d
ry c
at
food
for
you
r ca
t. T
he
fun
ctio
n
c=
6.3
– 0
.25p
rep
rese
nts
th
e am
oun
t of
ca
t fo
od c
rem
ain
ing i
n t
he
bag w
hen
th
e ca
t is
fed
th
e sa
me
am
oun
t ea
ch d
ay f
or
p d
ays.
Fin
d t
he
zero
of
this
fu
nct
ion
. D
escr
ibe
wh
at
this
valu
e m
ean
s in
th
is c
onte
xt.
2
. S
AV
ING
S J
essi
ca i
s sa
vin
g f
or c
olle
ge
usi
ng a
dir
ect
dep
osit
fro
m h
er p
aych
eck
in
to a
savin
gs
acc
oun
t. T
he
fun
ctio
n
m =
3045 -
52.5
0t
rep
rese
nts
th
e am
oun
t of
mon
ey m
sti
ll n
eed
ed a
fter
t
wee
ks.
Fin
d t
he
zero
of
this
fu
nct
ion
. W
hat
doe
s th
is v
alu
e m
ean
in
th
is
con
text?
3
. FIN
AN
CE
Mic
hael
bor
row
s $100 f
rom
h
is d
ad
. T
he
fun
ctio
n v
= 1
00 -
4.7
5p
re
pre
sen
ts t
he
outs
tan
din
g b
ala
nce
v a
fter
p w
eek
ly p
aym
ents
. F
ind
th
e ze
ro o
f th
is f
un
ctio
n. D
escr
ibe
wh
at
this
valu
e m
ean
s in
th
is c
onte
xt.
4. B
AK
E S
ALE
A
shle
y h
as
$15 i
n t
he
Pep
C
lub t
reasu
ry t
o p
ay f
or s
up
pli
es f
or a
ch
ocol
ate
ch
ip c
ook
ie b
ak
e sa
le. T
he
fun
ctio
n d
= 1
5 –
0.0
8c
rep
rese
nts
th
e d
olla
rs d
lef
t in
th
e cl
ub t
reasu
ry a
fter
m
ak
ing c
coo
kie
s. F
ind
th
e ze
ro o
f th
is
fun
ctio
n. W
hat
doe
s th
is v
alu
e re
pre
sen
t in
th
is c
onte
xt?
5
. D
EN
TA
L H
YG
IEN
EY
ou a
re p
ack
ing
you
r su
itca
se t
o go
aw
ay t
o a 1
4-d
ay
sum
mer
cam
p. T
he
stor
e ca
rrie
s th
ree
size
s of
tu
bes
of
toot
hp
ast
e.
Tu
be
Siz
e
(ou
nc
es
)
Siz
e
(gra
ms
)
A0
.75
21.
26
B0
.92
5.5
2
C3
.08
5.0
4
So
urc
e:
National A
cadem
y o
f S
cie
nces
a.
Th
e fu
nct
ion
n=
21.2
6 -
0.8
b
rep
rese
nts
th
e n
um
ber
of
rem
ain
ing
bru
shin
gs
n u
sin
g b
gra
ms
per
bru
shin
g u
sin
g T
ube
A. F
ind
th
e ze
ro
of t
his
fu
nct
ion
. D
escr
ibe
wh
at
this
valu
e m
ean
s in
th
is c
onte
xt.
b.
Th
e fu
nct
ion
n=
25.5
2 –
0.8
b
rep
rese
nts
th
e n
um
ber
of
rem
ain
ing
bru
shin
gs
n u
sin
g b
gra
ms
per
bru
shin
g u
sin
g T
ube
B. F
ind
th
e ze
ro
of t
his
fu
nct
ion
. D
escr
ibe
wh
at
this
valu
e m
ean
s in
th
is c
onte
xt.
c.
Wri
te a
fu
nct
ion
to
rep
rese
nt
the
nu
mber
of
rem
ain
ing b
rush
ings
n u
sin
g b
gra
ms
per
bru
shin
g u
sin
g
Tu
be
C. F
ind
th
e ze
ro o
f th
is f
un
ctio
n.
Des
crib
e w
hat
this
valu
e m
ean
s in
th
is c
onte
xt.
d.
If y
ou w
ill
bru
sh y
our
teet
h t
wic
e ea
ch
day w
hil
e at
cam
p, w
hic
h i
s th
e sm
all
est
tube
of t
ooth
past
e you
can
ch
oose
? E
xp
lain
you
r re
aso
nin
g.
3-2 25.2
; T
here
are
25 f
ull s
erv
ing
s
of
cat
foo
d i
n t
heb
ag
.
58;
It w
ill
take 5
8 w
eeks f
or
Jessic
a t
o s
ave t
he m
on
ey s
he
need
s.
$21.
05; A
fter
21 w
eeks, h
e w
ill
have p
aid
back 2
1 ×
4.7
5, o
r $99.7
5. H
e p
ays $
0.2
5 o
n w
eek 2
2.
187.
5, S
he b
reaks e
ven
at
188 c
oo
kie
s.
n =
85.0
4 -
0.8
b;
106; Tu
be C
w
ill
pro
vid
e 1
06 b
rush
ing
s.
31.
9; Tu
be B
will
pro
vid
e
31 b
rush
ing
s.
26.5
75; Tu
be A
will
pro
vid
e
26 b
rush
ing
s.
Tu
be B
; Yo
u n
eed
28 b
rush
ing
s.
Tu
be A
is n
ot
en
ou
gh
an
d
Tu
be C
is t
oo
mu
ch
.
Lesson 3-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
17
G
len
co
e A
lge
bra
1
3-2
En
ric
hm
en
t
Co
mp
osit
e F
un
cti
on
s
Th
ree
thin
gs
are
nee
ded
to
have
a f
un
ctio
n—
a s
et c
all
ed t
he
dom
ain
, a s
et c
all
ed t
he
ran
ge,
an
d a
ru
le t
hat
matc
hes
each
ele
men
t in
th
e d
omain
wit
h o
nly
on
e el
emen
t in
th
e ra
nge.
Her
e is
an
exam
ple
.
Ru
le: f(
x)
= 2
x +
1
3 5
-5
f(x)
x 1 2
-3
f(x
) =
2x +
1
f(1
) =
2(1
) +
1 =
2 +
1 =
3
f(2
) =
2(2
) +
1 =
4 +
1 =
5
f(-
3)
= 2
(-3)
+ 1
= 2
6 +
1 =
-5
Su
pp
ose
we
have
thre
e se
ts A
, B
, an
d C
an
d t
wo
fun
ctio
ns
des
crib
ed
as
show
n b
elow
.
Ru
le: f(
x)
= 2
x +
1
Ru
le: g
(y)
= 3
y -
4
AB
C
f(x) 3
5
x 1
g[f
(x)]
g
(y)
= 3
y -
4
g
(3)
= 3
(3)
- 4
= 5
Let
’s f
ind
a r
ule
th
at
wil
l m
atc
h e
lem
ents
of
set
A w
ith
ele
men
ts o
f se
t C
wit
hou
t fi
nd
ing a
ny e
lem
ents
in
set
B. In
oth
er w
ord
s, l
et’s
fin
d
a r
ule
for
th
e co
mp
osit
e f
un
cti
on
g[f(x
)].
Sin
ce f
(x)
= 2
x +
1, g[f
(x)]
= g
(2x +
1).
Sin
ce g
(y)
= 3
y -
4, g
(2x +
1)
= 3
(2x +
1)
- 4
, or
6x -
1.
Th
eref
ore,
g[f
(x)]
= 6
x -
1.
Fin
d a
ru
le f
or t
he
co
mp
osit
e f
un
cti
on
g[f
(x)]
.
1. f(
x)
= 3
x a
nd
g(y
) =
2y +
1
2. f(
x)
= x
2 +
1 a
nd
g(y
) =
4y
3. f(
x)
= -
2x a
nd
g(y
) =
y2 -
3y
4. f(
x)
=
1
−
x -
3 a
nd
g(y
) =
y-
1
5. Is
it
alw
ays
the
case
th
at
g[f
(x)]
= f
[g(x
)]?
Ju
stif
y y
our
an
swer
.
g[f
(x)]
= 6
x +
1
g[f
(x)]
= 4
x2 +
4
g[f
(x)]
= 4
x2 +
6x
g[f
(x)]
= x
- 3
N
o. F
or
exam
ple
, in
Exerc
ise 1
,
f[g
(x)]
= f
(2x +
1)
= 3
(2x +
1)
= 6
x +
3, n
ot
6x +
1.
Answers (Lesson 3-2)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A8 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
18
G
len
co
e A
lge
bra
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Rate
of
Ch
an
ge a
nd
Slo
pe
3-3
Ra
te o
f C
ha
ng
e
Th
e r
ate
of
ch
an
ge t
ell
s, o
n a
vera
ge, h
ow
a q
uan
tity
is
chan
gin
g
over
tim
e.
P
OP
ULA
TIO
N T
he
gra
ph
sh
ow
s t
he
po
pu
lati
on
gro
wth
in
Ch
ina
.
a
. F
ind
th
e r
ate
s o
f ch
an
ge
fo
r 1
95
0–1
97
5 a
nd
fo
r
20
00
–2
02
5.
1950–1975: ch
an
ge i
n p
op
ula
tion
−
−
ch
an
ge i
n t
ime
=
0.9
3 -
0.5
5
−
1975 -
1950
= 0
.38
−
25 o
r 0.0
152
2000–2025: ch
an
ge i
n p
op
ula
tion
−
−
ch
an
ge i
n t
ime
=
1.4
5 -
1.2
7
−
2025
- 2
000
= 0
.18
−
25 o
r 0.0
072
b
. E
xp
lain
th
e m
ea
nin
g o
f th
e r
ate
of
ch
an
ge
in
ea
ch
ca
se
.
Fro
m 1
950–1975, th
e g
row
th w
as
0.0
152 b
illi
on
per
year,
or
15.2
mil
lion
per
year.
Fro
m 2
000–2025, th
e g
row
th i
s exp
ect
ed
to b
e 0
.0072 b
illi
on
per
year,
or
7.2
mil
lion
p
er
year.
c.
Ho
w a
re
th
e d
iffe
re
nt
ra
tes o
f ch
an
ge
sh
ow
n o
n t
he
gra
ph
?
Th
ere
is
a g
reate
r vert
ical
chan
ge f
or
1950–1975 t
han
for
2000–2025. T
here
fore
, th
e
sect
ion
of
the g
rap
h f
or
1950–1975 h
as
a s
teep
er
slop
e.
Exerc
ises
1. LO
NG
EV
ITY
T
he g
rap
h s
how
s th
e p
red
icte
d l
ife
exp
ect
an
cy f
or
men
an
d w
om
en
born
in
a g
iven
year.
a
. F
ind
th
e r
ate
s of
chan
ge f
or
wom
en
fro
m 2
000–2025
an
d 2
025–2050.
0.1
6/y
r, 0
.12/y
r
b
. F
ind
th
e r
ate
s of
chan
ge f
or
men
fro
m 2
000–2025 a
nd
2025–2050.
0.1
6/y
r, 0
.12/y
r
c.
Exp
lain
th
e m
ean
ing o
f you
r re
sult
s in
Exerc
ises
1
an
d 2
. B
oth
men
an
d w
om
en
in
cre
ased
th
eir
life
exp
ecta
ncy a
t th
e s
am
e r
ate
s.
d. W
hat
patt
ern
do y
ou
see i
n t
he i
ncr
ease
wit
h e
ach
25-y
ear
peri
od
? W
hile l
ife e
xp
ecta
ncy
incre
ases, it
do
es n
ot
incre
ase a
t a
co
nsta
nt
rate
.
e.
Mak
e a
pre
dic
tion
for
the l
ife e
xp
ect
an
cy f
or
2050–2075. E
xp
lain
how
you
arr
ived
at
you
r p
red
icti
on
. S
am
ple
an
sw
er:
89 f
or
wo
men
an
d 8
3 f
or
men
; th
e
decre
ase i
n r
ate
fro
m 2
00
0–2025 t
o 2
025–2050 i
s 0
.04/y
r. I
f th
e d
ecre
ase
in t
he r
ate
rem
ain
s t
he s
am
e, th
e c
han
ge o
f ra
te f
or
2050–2075 m
igh
t b
e
0.0
8/y
r an
d 2
5(0
.08)
= 2
years
of
incre
ase o
ver
the 2
5-y
ear
sp
an
.
Pre
dic
tin
g L
ife E
xp
ecta
ncy
Year
Bo
rn
Age
2000
Women
Men
100
95
90
85
80
75
70
65
2050*
2025*
*Estim
ated
Sourc
e:
USA
TO
DA
Y80
84
81
78
74
87
Po
pu
lati
on
Gro
wth
in
Ch
ina
Year
People (billions)
1950
1975
2000
2.0
1.5
1.0
0.5 0
2025*
*Estim
ated
Sourc
e:
Uni
ted
Nat
ions
Pop
ulat
ion
Div
isio
n
0.55
0.93
1.27
1.45
Exam
ple
Lesson 3-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
19
G
len
co
e A
lge
bra
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Rate
of
Ch
an
ge a
nd
Slo
pe
3-3
Fin
d S
lop
e
Th
e s
lop
e o
f a l
ine i
s th
e r
ati
o o
f ch
an
ge i
n t
he y
- coord
inate
s (r
ise)
to t
he
chan
ge i
n t
he x
- coord
inate
s (r
un
) as
you
move i
n t
he p
osi
tive d
irect
ion
.
Slo
pe
of
a L
ine
m =
rise
−
run o
r m
= y
2 -
y 1
−
x 2 -
x 1 , w
he
re (
x1,
y1)
an
d (
x2,
y2)
are
th
e c
oo
rdin
ate
s
of
any t
wo
po
ints
on
a n
onve
rtic
al lin
e
F
ind
th
e s
lop
e o
f th
e
lin
e t
ha
t p
asse
s t
hro
ug
h (
-3
, 5
) a
nd
(4
, -
2).
Let
(-3, 5)
= (
x1, y
1)
an
d
(4,
-2)
= (
x2, y
2).
m =
y2 -
y1
−
x2 -
x1
S
lope form
ula
=
-
2 -
5
−
4 -
(-
3)
y 2 =
-2,
y 1 =
5,
x 2 =
4,
x 1 =
-3
=
-7
−
7
Sim
plif
y.
=
-1
Exerc
ises
Fin
d t
he
slo
pe
of
the
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
1. (4
, 9),
(1, 6)
1
2. (-
4,
-1),
(-
2,
-5)
- 2
3. (-
4,
-1),
(-
4,
-5)
u
nd
e!
ned
4. (2
, 1),
(8, 9)
4
−
3
5. (1
4,
-8),
(7,
-6)
- 2
−
7
6. (4
, -
3),
(8,
-3)
0
7. (1
, -
2),
(6, 2)
4
−
5
8. (2
, 5),
(6, 2)
- 3
−
4
9. (4
, 3.5
), (
-4, 3.5
) 0
Fin
d t
he
va
lue
of r s
o t
he
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts h
as t
he
g
ive
n s
lop
e.
10. (6
, 8),
(r,
-2),
m =
1
-4
11. (-
1,
-3),
(7, r)
, m
= 3
−
4 3
12. (2
, 8),
(r,
-4)
m =
-3 6
13. (7
, -
5),
(6, r)
, m
= 0
-
5
14. (r
, 4),
(7, 1),
m =
3
−
4 11
15. (7
, 5),
(r,
9),
m =
6 2
3
−
3
F
ind
th
e v
alu
e o
f r s
o t
ha
t th
e l
ine
th
ro
ug
h (
10
, r)
an
d (
3,
4)
ha
s a
slo
pe
of
- 2
−
7 .
m
= y
2 -
y1
−
x2 -
x1
Slo
pe form
ula
-
2
−
7 =
4 -
r
−
3 -
10
m =
- 2
−
7 ,
y2 =
4,
y1 =
r,
x2 =
3,
x1 =
10
-
2
−
7 =
4 -
r
−
-7
Sim
plif
y.
-2(-
7)
= 7
(4 -
r)
Cro
ss m
ultip
ly.
14 =
28 -
7r
Dis
trib
utive
Pro
pert
y
-
14 =
-7
r S
ubtr
act
28 f
rom
each s
ide.
2 =
r
Div
ide e
ach s
ide b
y -
7.
Exam
ple
1Exam
ple
2
Answers (Lesson 3-3)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A9 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
20
G
len
co
e A
lge
bra
1
Sk
ills
Practi
ce
Rate
of
Ch
an
ge a
nd
Slo
pe
3-3
Fin
d t
he
slo
pe
of
the
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
1.
( 0, 1
)
( 2, 5
)
x
y O
2.
( 0, 0
)
( 3, 1
)
x
y
O
3.
( 0,
1) ( 1, -
2)
x
y
O
2
1
−
3
-
3
4. (2
, 5),
(3, 6)
1
5. (6
, 1),
(-
6, 1)
0
6. (4
, 6),
(4, 8)
un
de!
ned
7. (5
, 2),
(5,
-2)
un
de!
ned
8. (2
, 5),
(-
3,
-5)
2
9. (9
, 8),
(7,
-8)
8
10. (-
5,
-8),
(-
8, 1)
-3
11. (-
3, 10),
(-
3, 7)
un
de!
ned
12. (1
7, 18),
(18, 17)
-1
13. (-
6,
-4),
(4, 1)
1
−
2
14. (1
0, 0),
(-
2, 4)
- 1
−
3
15. (2
, -
1),
(-
8,
-2)
1
−
10
16. (5
, -
9),
(3,
-2)
- 7
−
2
17. (1
2, 6),
(3,
-5)
11
−
9
18. (-
4, 5),
(-
8,
-5)
5
−
2
19. (-
5, 6),
(7,
-8)
- 7
−
6
Fin
d t
he
va
lue
of r s
o t
he
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts
ha
s t
he
giv
en
slo
pe
.
20. (r
, 3),
(5, 9),
m =
2 2
21. (5
, 9),
(r,
-3),
m =
-4 8
22. (r
, 2),
(6, 3),
m =
1
−
2 4
23. (r
, 4),
(7, 1),
m =
3
−
4
11
24. (5
, 3),
(r,
-5),
m =
4 3
25. (7
, r)
, (4
, 6),
m =
0 6
Lesson 3-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
21
G
len
co
e A
lge
bra
1
Practi
ce
Rate
of
Ch
an
ge a
nd
Slo
pe
3-3
Fin
d t
he
slo
pe
of
the
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
1.
( –1,
0)
( –2,
3)
x
y
O
2.
( 3,
1)
( –2
, –
3)
x
y
O
3.
( –2,
3)
( 3,
3)
x
y O
-
3
4
−
5
0
4. (6
, 3),
(7,
-4)
-7
5. (-
9,
-3),
(-
7,
-5)
-1
6. (6
, -
2),
(5,
-4)
2
7. (7
, -
4),
(4, 8)
-4
8. (-
7, 8),
(-
7, 5)
un
de!
ned
9. (5
, 9),
(3, 9)
0
10. (1
5, 2),
(-
6, 5)
- 1
−
7
11. (3
, 9),
(-
2, 8)
1
−
5
12. (-
2,
-5),
(7, 8)
13
−
9
13. (1
2, 10),
(12, 5)
un
de!
ned
14. (0
.2,
-0.9
), (
0.5
, -
0.9
) 0
15. ( 7
−
3 ,
4
−
3 ) ,
(- 1
−
3 ,
2
−
3 )
1
−
4
Fin
d t
he
va
lue
of r s
o t
he
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts h
as t
he
giv
en
slo
pe
.
16. (-
2, r)
, (6
, 7),
m =
1
−
2 3
17. (-
4, 3),
(r,
5),
m =
1
−
4 4
18. (-
3,
-4),
(-
5, r)
, m
= -
9
−
2 5
19.
(-5, r)
, (1
, 3),
m =
7
−
6
-4
20. (1
, 4),
(r,
5),
m u
nd
efi
ned
1
21. (-
7, 2),
(-
8, r)
, m
= -
5 7
22. (r
, 7),
(11, 8),
m =
- 1
−
5 16
23. (r
, 2),
(5, r)
, m
= 0
2
24. R
OO
FIN
G T
he pitch
of
a r
oof
is t
he n
um
ber
of
feet
the r
oof
rise
s fo
r each
12 f
eet
hori
zon
tall
y. I
f a r
oof
has
a p
itch
of
8, w
hat
is i
ts s
lop
e e
xp
ress
ed
as
a p
osi
tive n
um
ber?
2
−
3
25. S
ALE
S A
dail
y n
ew
spap
er
had
12,1
25 s
ubsc
ribers
wh
en
it
began
pu
bli
cati
on
. F
ive y
ears
la
ter
it h
ad
10,1
00 s
ubsc
ribers
. W
hat
is t
he a
vera
ge y
earl
y r
ate
of
chan
ge i
n t
he n
um
ber
of
subsc
ribers
for
the f
ive-y
ear
peri
od
? -
405 s
ub
scri
bers
per
year
Answers (Lesson 3-3)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A10 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
22
G
len
co
e A
lge
bra
1
Wo
rd
Pro
ble
m P
racti
ce
Rate
of
Ch
an
ge a
nd
Slo
pe
3-3
1.H
IGH
WA
YS
Roa
dw
ay s
ign
s su
ch a
s th
e on
e bel
ow a
re u
sed
to
warn
dri
ver
s of
an
u
pco
min
g s
teep
dow
n g
rad
e th
at
cou
ld
lead
to
a d
an
ger
ous
situ
ati
on. W
hat
is
the
gra
de,
or
slop
e, o
f th
e h
ill
des
crib
ed
on t
he
sign
?2 − 25
2. A
MU
SE
ME
NT
PA
RK
S T
he
Sh
eiK
ra
roll
er c
oast
er a
t B
usc
h G
ard
ens
in
Tam
pa, F
lori
da, fe
atu
res
a 1
38-f
oot
ver
tica
l d
rop. W
hat
is t
he
slop
e of
th
e co
ast
er t
rack
at
this
part
of
the
rid
e?
Exp
lain
.
T
he s
lop
e i
s u
nd
e!
ned
becau
se
the d
rop
is v
ert
ical.
3. C
EN
SU
S T
he
table
sh
ows
the
pop
ula
tion
d
ensi
ty f
or t
he
state
of
Tex
as
in v
ari
ous
yea
rs. F
ind
th
e aver
age
an
nu
al
rate
of
chan
ge
in t
he
pop
ula
tion
den
sity
fro
m
2000 t
o 2009.
in
cre
ased
ab
ou
t 1.
9 p
eo
ple
per
sq
uare
mile
4.R
EA
L E
STA
TE
A r
ealt
or e
stim
ate
s th
e m
edia
n p
rice
of
an
exis
tin
g s
ingle
-fam
ily
hom
e in
Ced
ar
Rid
ge
is $
221,9
00. T
wo
yea
rs a
go,
th
e m
edia
n p
rice
was
$195,2
00. F
ind
th
e aver
age
an
nu
al
rate
of
ch
an
ge
in m
edia
n h
ome
pri
ce i
n t
hes
e
yea
rs. $
13,3
50
5. C
OA
L E
XP
OR
TS
Th
e gra
ph
sh
ows
the
an
nu
al
coal
exp
orts
fro
m U
.S. m
ines
in
m
illi
ons
of s
hor
t to
ns.
S
ou
rce:
Energ
y In
form
atio
n A
ssoci
atio
n
a.
Wh
at
was
the
rate
of
chan
ge
in c
oal
exp
orts
bet
wee
n 2
001 a
nd
2002?
-9 m
illio
n t
on
s p
er
year
or
- 9
−
1
b.
How
doe
s th
e ra
te o
f ch
an
ge
in c
oal
exp
orts
fro
m 2
005 t
o 2006 c
omp
are
to
that
of 2
001 t
o 2002?
In 2
005–20
06, th
e r
ate
was
0 c
om
pare
d t
o -
9
−
1 i
n
20
01–20
02.
c.
Exp
lain
th
e m
ean
ing o
f th
e p
art
of
the
gra
ph
wit
h a
slo
pe
of z
ero.
Th
e s
lop
e i
nd
icate
s t
hat
there
w
as n
o c
han
ge i
n t
he a
mo
un
t o
f co
al
exp
ort
ed
betw
een
20
05
an
d 2
006.
Million Short Tons
40
50
30 0
60
70
80
90
100
2004
2003
2000
2001
2002
2006
2005
Tota
l Exp
ort
s
Po
pu
lati
on
De
ns
ity
Ye
ar
Pe
op
le P
er
Sq
ua
re M
ile
19
30
22
.1
19
60
36
.4
19
80
54
.3
20
00
79
.6
20
09
96
.7
So
urce:
Bure
au o
f th
e C
ensu
s, U
.S. D
ept.
of C
om
merc
e
Lesson 3-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
23
G
len
co
e A
lge
bra
1
3-3
En
ric
hm
en
t
Treasu
re H
un
t w
ith
Slo
pes
Usin
g t
he
de
fin
itio
n o
f slo
pe
, d
ra
w s
eg
me
nts
wit
h t
he
slo
pe
s l
iste
d
be
low
in
ord
er.
A c
orre
ct
so
luti
on
wil
l tr
ace
th
e r
ou
te t
o t
he
tre
asu
re
.
1. 3
2.
1
−
4
3.
- 2
−
5
4.
0
5. 1
6.
-1
7.
no
slop
e 8.
2
−
7
9.
3
−
2
10.
1
−
3
11.
- 3
−
4
12.
3
Sta
rt H
ere
Trea
sure
Answers (Lesson 3-3)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A11 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
24
G
len
co
e A
lge
bra
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Dir
ect
Vari
ati
on
3-4
Dir
ect
Va
ria
tio
n E
qu
ati
on
s A
dir
ect
va
ria
tio
n i
s d
escr
ibed
by a
n e
qu
ati
on o
f th
e fo
rm y
= k
x, w
her
e k ≠
0. W
e sa
y t
hat
y v
ari
es d
irec
tly a
s x. In
th
e eq
uati
on y
= k
x, k i
s th
e co
nsta
nt
of
va
ria
tio
n.
N
am
e t
he
co
nsta
nt
of
va
ria
tio
n f
or t
he
eq
ua
tio
n. T
he
n f
ind
the
slo
pe
of
the
lin
e t
ha
t p
asse
s
thro
ug
h t
he
pa
ir o
f p
oin
ts.
For
y =
1
−
2 x
, th
e co
nst
an
t of
vari
ati
on i
s 1
−
2 .
m
= y
2 -
y 1
−
x 2 -
x 1
Slo
pe form
ula
=
1 -
0
−
2 -
0
(x1,
y1)
= (
0,
0),
(x
2,
y2)
= (
2,
1)
=
1
−
2
Sim
plif
y.
Th
e sl
ope
is 1
−
2 .
S
up
po
se
y v
arie
s d
ire
ctl
y
as x
, a
nd
y =
30
wh
en
x =
5.
a.
Writ
e a
dir
ect
va
ria
tio
n e
qu
ati
on
tha
t re
late
s x
an
d y
.
Fin
d t
he
valu
e of
k.
y =
kx
Direct
vari
ation e
quation
30 =
k(5
) R
epla
ce y
with 3
0 a
nd x
with 5
.
6 =
k
Div
ide e
ach s
ide b
y 5
.
Th
eref
ore,
th
e eq
uati
on i
s y =
6x.
b.
Use
th
e d
ire
ct
va
ria
tio
n e
qu
ati
on
to
fin
d x
wh
en
y =
18
.
y =
6x
Direct
vari
ation e
quation
18 =
6x
Repla
ce y
with 1
8.
3 =
x
Div
ide e
ach s
ide b
y 6
.
Th
eref
ore,
x =
3 w
hen
y =
18.
Exerc
ises
Na
me
th
e c
on
sta
nt
of
va
ria
tio
n f
or e
ach
eq
ua
tio
n. T
he
n d
ete
rm
ine
th
e s
lop
e o
f th
e
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
1.
2.
( 1, 3
)
( 0, 0
)x
y
O
y =
3x
3.
-2;
-2
3;
3
3
−
2 ; 3
−
2
Su
pp
ose
y v
arie
s d
ire
ctl
y a
s x
. W
rit
e a
dir
ect
va
ria
tio
n e
qu
ati
on
th
at
re
late
s x
to
y.
Th
en
so
lve
.
4. If
y =
4 w
hen
x =
2, fi
nd
y w
hen
x =
16.
y =
2x;
32
5. If
y =
9 w
hen
x =
-3, fi
nd
x w
hen
y =
6.
y =
-3x;
-2
6. If
y =
-4.8
wh
en x
= -
1.6
, fi
nd
x w
hen
y =
-24.
y =
3x;
-8
7. If
y =
1
−
4 w
hen
x =
1
−
8 ,
fin
d x
wh
en y
=
3
−
16 .
y =
2x;
3
−
32
( –2,
–3)
( 0,
0)
x
y O
y =
3 2x
( –1
, 2
)
( 0, 0
)
x
y
O
y =
–2
x
( 2, 1
)
( 0, 0
)x
y
Oy =
1 2x
Exam
ple
1Exam
ple
2
Lesson 3-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
25
G
len
co
e A
lge
bra
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Dir
ect
Vari
ati
on
3-4
Dir
ect
Va
ria
tio
n P
rob
lem
s T
he
dis
tan
ce
fo
rm
ula
d =
rt
is a
dir
ect
vari
ati
on
equ
ati
on. In
th
e fo
rmu
la, d
ista
nce
d v
ari
es d
irec
tly a
s ti
me
t, a
nd
th
e ra
te r
is
the
con
stan
t of
vari
ati
on.
T
RA
VE
L A
fa
mil
y d
ro
ve
th
eir
ca
r 2
25
mil
es i
n 5
ho
urs.
a.
Writ
e a
dir
ect
va
ria
tio
n e
qu
ati
on
to
fin
d t
he
dis
tan
ce
tra
ve
led
fo
r a
ny
nu
mb
er
of
ho
urs.
Use
giv
en v
alu
es f
or d
an
d t
to
fin
d r
.
d
= r
t O
rigin
al equation
225 =
r(5
) d
= 2
25 a
nd t
= 5
45 =
r
Div
ide e
ach s
ide b
y 5
.
Th
eref
ore,
th
e d
irec
t vari
ati
on e
qu
ati
on i
s d
= 4
5t.
A
uto
mo
bil
e T
rip
s
Tim
e (
ho
urs
)
Distance (miles)
10
23
45
67
8t
d
360
270
180
90
( 1,
45)
( 5,
22
5)
d =
45
t
b.
Gra
ph
th
e e
qu
ati
on
.
Th
e gra
ph
of
d =
45
t p
ass
es t
hro
ugh
th
e or
igin
wit
h
slop
e 45.
m =
45
−
1
ri
se
−
run
✔C
HE
CK
(5, 225)
lies
on
th
e gra
ph
.
c.
Esti
ma
te h
ow
ma
ny
ho
urs i
t w
ou
ld t
ak
e t
he
fam
ily
to
driv
e 3
60
mil
es.
d
= 4
5t
Ori
gin
al equation
360 =
45
t R
epla
ce d
with 3
60.
t
= 8
D
ivid
e e
ach s
ide b
y 4
5.
Th
eref
ore,
it
wil
l ta
ke
8 h
ours
to
dri
ve
360 m
iles
.
Exerc
ises
1
. R
ETA
IL T
he
tota
l co
st C
of
bu
lk j
elly
bea
ns
is
$4.4
9 t
imes
th
e n
um
ber
of
pou
nd
s p
.
a.
Wri
te a
dir
ect
vari
ati
on e
qu
ati
on t
hat
rela
tes
the
vari
able
s.
C =
4.4
9p
b.
Gra
ph
th
e eq
uati
on o
n t
he
gri
d a
t th
e ri
gh
t.
c.
Fin
d t
he
cost
of
3
−
4 p
oun
d o
f je
lly b
ean
s. $
3.3
7
2. C
HE
MIS
TR
Y C
harl
es’s
Law
sta
tes
that,
at
a c
onst
an
t
pre
ssu
re, vol
um
e of
a g
as
V v
ari
es d
irec
tly a
s it
s te
mp
eratu
re T
. A
vol
um
e of
4 c
ubic
fee
t of
a c
erta
in
gas
has
a t
emp
eratu
re o
f 200 d
egre
es K
elvin
.
a.
Wri
te a
dir
ect
vari
ati
on e
qu
ati
on t
hat
rela
tes
the
vari
able
s.
V =
0.0
2T
b.
Gra
ph
th
e eq
uati
on o
n t
he
gri
d a
t th
e ri
gh
t.
c.
Fin
d t
he
vol
um
e of
th
e sa
me
gas
at
250 d
egre
es K
elvin
. 5 f
t3
Co
st
of
Jell
y B
ean
s
Weig
ht
(po
un
ds)
Cost (dollars)
20
4p
C
18.00
13.50
9.00
4.50
Ch
arl
es’s
Law
Tem
pera
ture
(K
)
Volume (cubic feet)
100
0200
T
V 4 3 2 1
Exam
ple
Answers (Lesson 3-4)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A12 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
26
G
len
co
e A
lge
bra
1
Sk
ills
Practi
ce
Dir
ect
Vari
ati
on
3-4
Na
me
th
e c
on
sta
nt
of
va
ria
tio
n f
or e
ach
eq
ua
tio
n. T
he
n d
ete
rm
ine
th
e s
lop
e o
f th
e
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
1.
( 3, 1
)
( 0, 0
)x
y O
y =
1 3 x
1
−
3 ; 1
−
3
2.
-2;
-2
3.
- 3
−
2 ;
Gra
ph
ea
ch
eq
ua
tio
n.
4. y =
3x
5. y =
- 3
−
4 x
6. y =
2
−
5 x
Su
pp
ose
y v
arie
s d
ire
ctl
y a
s x
. W
rit
e a
dir
ect
va
ria
tio
n e
qu
ati
on
th
at
re
late
s
x a
nd
y. T
he
n s
olv
e.
7. If
y =
-8 w
hen
x =
-2, fi
nd
x
8. If
y =
45 w
hen
x =
15, fi
nd
x
wh
en y
= 3
2.
y =
4x;
8
w
hen
y =
15.
y =
3x;
5
9. If
y =
-4 w
hen
x =
2, fi
nd
y
10. If
y =
-9 w
hen
x =
3, fi
nd
y
wh
en x
= -
6.
y =
-2x;
12
w
hen
x =
-5.
y =
-3x;
15
11. If
y =
4 w
hen
x =
16, fi
nd
y
12. If
y =
12 w
hen
x =
18, fi
nd
x
w
hen
x =
6.
y =
1
−
4 x
; 3
−
2
w
hen
y =
-16.
y =
2
−
3 x
; -
24
Writ
e a
dir
ect
va
ria
tio
n e
qu
ati
on
th
at
re
late
s t
he
va
ria
ble
s.
Th
en
gra
ph
th
e e
qu
ati
on
.
13. T
RA
VE
L T
he
tota
l co
st C
of
gaso
lin
e
14. S
HIP
PIN
G T
he
nu
mber
of
del
iver
ed t
oys
T
is $
3.0
0 t
imes
th
e n
um
ber
of
gall
ons
g.
is
3 t
imes
th
e to
tal
nu
mber
of
crate
s c.
Gaso
lin
e C
ost
Gallo
ns
Cost ($)
20
46
71
35
g
C
28
24
20
16
12 8 4
C =
3.0
0g
Toys S
hip
ped
Cra
tes
Toys
20
46
71
35
c
T
21
18
15
12 9 6 3
T
= 3
c
x
y
Ox
y
Ox
y
O
( –2,
3)
( 0,
0)
x
y
O
y =
– 3 2
x
( -1, 2
)( 0
, 0
)
x
y
O
y =
-2
x
- 3
−
2
Lesson 3-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
27
G
len
co
e A
lge
bra
1
3-4
Practi
ce
Dir
ect
Vari
ati
on
Na
me
th
e c
on
sta
nt
of
va
ria
tio
n f
or e
ach
eq
ua
tio
n. T
he
n d
ete
rm
ine
th
e s
lop
e o
f th
e
lin
e t
ha
t p
asse
s t
hro
ug
h e
ach
pa
ir o
f p
oin
ts.
1.
( 4,
3)
( 0,
0)
x
y O
y =
3 x
4
2.
( 3,
4)
( 0,
0)
x
y O
y =
4 3x
3.
( –2
, 5)
( 0,
0)
x
y
O
y =
- 5 2
x
Gra
ph
ea
ch
eq
ua
tio
n.
4. y =
-2
x
5. y =
6
−
5 x
6. y =
- 5
−
2 x
Su
pp
ose
y v
arie
s d
ire
ctl
y a
s x
. W
rit
e a
dir
ect
va
ria
tio
n e
qu
ati
on
th
at
re
late
s
x a
nd
y. T
he
n s
olv
e.
7. If
y =
7.5
wh
en x
= 0
.5, fi
nd
y w
hen
x =
-0.3
. y =
15x;
- 4
.5
8. If
y =
80 w
hen
x =
32, fi
nd
x w
hen
y =
100.
y =
2.5
x;
40
9. If
y =
3
−
4 w
hen
x =
24, fi
nd
y w
hen
x =
12.
y =
1
−
32 x
; 3
−
8
Writ
e a
dir
ect
va
ria
tio
n e
qu
ati
on
th
at
re
late
s t
he
va
ria
ble
s. T
he
n g
ra
ph
th
e
eq
ua
tio
n.
10. M
EA
SU
RE
Th
e w
idth
W o
f a
11. T
ICK
ET
S T
he
tota
l co
st C
of
tick
ets
isre
ctan
gle
is
two
thir
ds
of t
he
len
gth
ℓ.
$4.5
0 t
imes
th
e n
um
ber
of
tick
ets
t.
W
= 2
−
3 ℓ
C =
4.5
0t
12. P
RO
DU
CE
Th
e co
st o
f ban
an
as
vari
es d
irec
tly w
ith
th
eir
wei
gh
t. M
igu
el b
ough
t
3 1
−
2 p
oun
ds
of b
an
an
as
for
$1.1
2. W
rite
an
equ
ati
on t
hat
rela
tes
the
cost
of
the
ban
an
as
to t
hei
r w
eigh
t. T
hen
fin
d t
he
cost
of
4 1
−
4 p
oun
ds
of b
an
an
as.
C =
0.3
2p
; $1.
36
x
y
O
x
y
Ox
y
O
Co
st
of
Tic
kets
Tic
kets
Cost ($)
20
46
13
5t
C
25
20
15
10 5
Recta
ng
le D
imen
sio
ns
Len
gth
Width
40
812
26
10
ℓ
W 10 8 6 4 2
4
−
3 ; 4
−
3
- 5
−
2 ;
- 5
−
2
3
−
4 ;
3
−
4
Answers (Lesson 3-4)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A13 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
28
G
len
co
e A
lge
bra
1
Wo
rd
Pro
ble
m P
racti
ce
Dir
ect
Vari
ati
on
3-4
1. E
NG
INE
S T
he
engin
e of
a c
hain
saw
re
qu
ires
a m
ixtu
re o
f en
gin
e oi
l an
d
gaso
lin
e. A
ccor
din
g t
o th
e d
irec
tion
s, o
il
an
d g
aso
lin
e sh
ould
be
mix
ed a
s sh
own
in
th
e gra
ph
bel
ow. W
hat
is t
he
co n
stan
t of
vari
ati
on f
or t
he
lin
e gra
ph
ed?
2.5
2. R
AC
ING
In
a r
ecen
t yea
r, E
ngli
sh d
river
L
ewis
Ham
ilto
n w
on t
he
Un
ited
Sta
tes
Gra
nd
Pri
x a
t th
e In
dia
nap
olis
Mot
or
Sp
eed
way.
His
sp
eed
du
rin
g t
he
race
aver
aged
125.1
45 m
iles
per
hou
r. W
rite
a
dir
ect
vari
ati
on e
qu
ati
on f
or t
he
dis
tan
ce
d t
hat
Ham
ilto
n d
rove
in h
hou
rs a
t th
at
spee
d.
3. C
UR
RE
NC
Y T
he
exch
an
ge
rate
fro
m o
ne
curr
ency
to
an
oth
er v
ari
es e
ver
y d
ay.
R
ecen
tly t
he
exch
an
ge
rate
fro
m U
.S.
dol
lars
to
Bri
tish
pou
nd
ste
rlin
g (£
) w
as
$1.5
8 t
o £
1. W
rite
an
d s
olve
a d
irec
t vari
ati
on e
qu
ati
on t
o d
eter
min
e h
ow
man
y p
oun
ds
ster
lin
g y
ou w
ould
rec
eive
in e
xch
an
ge
for
$90 o
f U
.S. cu
rren
cy.
4. S
ALA
RY
Hen
ry s
tart
ed a
new
job
in
w
hic
h h
e is
paid
$9.5
0 a
n h
our.
Wri
te
an
d s
olve
an
equ
ati
on t
o d
eter
min
e H
enry
’s g
ross
sala
ry f
or a
40-h
our
wor
k w
eek
.
5
. S
ALE
S T
AX
Am
elia
rec
eived
a g
ift
card
to
a l
ocal
mu
sic
shop
for
her
bir
thd
ay.
S
he
pla
ns
to u
se t
he
gif
t ca
rd t
o bu
y
som
e n
ew C
Ds.
a.
Am
elia
ch
ose
3 C
Ds
that
each
cos
t $16. T
he
sale
s ta
x o
n t
he
thre
e C
Ds
is $
3.9
6. W
rite
a d
irec
t vari
ati
on
equ
ati
on r
elati
ng s
ale
s ta
x t
o th
e p
rice
.
b.
Gra
ph
th
e eq
uati
on y
ou w
rote
in
p
art
a.
c.
Wh
at
is t
he
sale
s ta
x r
ate
th
at
Am
elia
is
payin
g o
n t
he
CD
s?
Oil (fl oz)
34 2 159
10 8 7 6
Gaso
lin
e (
gal)
32
10
54
x
y
6
Pri
ce (
$)
30
20
10
50
40
90
80
70
100
P60
Sales Tax ($)
34 2 15T 8 7 6
d =
125.1
45
h
u =
1.5
8b
; ab
ou
t £
56.9
6
p =
9.5
h;
$380
T =
0.0
825P
8.2
5%
Lesson 3-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
29
G
len
co
e A
lge
bra
1
En
ric
hm
en
t 3
-4
nth
Po
wer
Vari
ati
on
An
equ
ati
on o
f th
e fo
rm y
= kxn, w
her
e k
≠ 0
, d
escr
ibes
an
nth
pow
er v
ari
ati
on. T
he
vari
able
n c
an
be
rep
lace
d b
y 2
to
ind
icate
th
e se
con
d p
ower
of x (
the
squ
are
of x)
or b
y 3
to
ind
icate
th
e th
ird
pow
er o
f x (
the
cube
of x
).
Ass
um
e th
at
the
wei
gh
t of
a p
erso
n o
f aver
age
bu
ild
vari
es d
irec
tly a
s th
e cu
be
of t
hat
per
son
’s h
eigh
t. T
he
equ
ati
on o
f vari
ati
on h
as
the
form
w =
kh
3.
Th
e w
eigh
t th
at
a p
erso
n’s
leg
s w
ill
sup
por
t is
pro
por
tion
al
to t
he
cros
s-se
ctio
nal
are
a o
f th
e le
g b
ones
. Th
is a
rea v
ari
es d
irec
tly a
s th
e sq
uare
of
the
per
son
’s h
eigh
t. T
he
equ
ati
on o
f vari
ati
on h
as
the
form
s =
kh
2.
An
sw
er e
ach
qu
esti
on
.
1. F
or a
per
son
6 f
eet
tall
wh
o w
eigh
s 200 p
oun
ds,
fin
d a
valu
e fo
r k i
n t
he
equ
ati
on w
= kh
3.
k =
0.9
3
2. U
se y
our
an
swer
fro
m E
xer
cise
1 t
o p
red
ict
the
wei
gh
t of
a p
erso
n w
ho
is 5
fee
t ta
ll.
ab
ou
t 11
6 p
ou
nd
s
3. F
ind
th
e valu
e fo
r k i
n t
he
equ
ati
on w
= kh
3 f
or a
baby w
ho
is 2
0 i
nch
es
lon
g a
nd
wei
gh
s 6 p
oun
ds.
k
= 1
.296 f
or
h =
5
−
3 f
t
4. H
ow d
oes
you
r an
swer
to
Exer
cise
3 d
emon
stra
te t
hat
a b
aby i
s si
gn
ific
an
tly f
att
er i
n p
rop
orti
on t
o it
s h
eigh
t th
an
an
ad
ult
?
k
has a
gre
ate
r valu
e.
5. F
or a
per
son
6 f
eet
tall
wh
o w
eigh
s 200 p
oun
ds,
fin
d a
valu
e fo
r k
in
th
e eq
uati
on s
= kh
2.
k
= 5
.56
6. F
or a
baby w
ho
is 2
0 i
nch
es l
ong a
nd
wei
gh
s 6 p
oun
ds,
fin
d a
n “
infa
nt
valu
e” f
or k
in
th
e eq
uati
on s
= kh
2.
k
= 2
.16 f
or
h =
5
−
3 f
t
7. A
ccor
din
g t
o th
e ad
ult
equ
ati
on y
ou f
oun
d (
Exer
cise
1),
how
mu
ch
wou
ld a
n i
magin
ary
gia
nt
20 f
eet
tall
wei
gh
?
74
40 p
ou
nd
s
8. A
ccor
din
g t
o th
e ad
ult
equ
ati
on f
or w
eigh
t su
pp
orte
d (
Exer
cise
5),
how
m
uch
wei
gh
t co
uld
a 2
0-f
oot
tall
gia
nt’
s le
gs
act
uall
y s
up
por
t?
o
nly
2224 p
ou
nd
s
9. W
hat
can
you
con
clu
de
from
Exer
cise
s 7 a
nd
8?
A
nsw
ers
will
vary
. F
or
exam
ple
, b
on
e s
tren
gth
lim
its t
he s
ize h
um
an
s
can
att
ain
.
Answers (Lesson 3-4)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A14 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
30
G
len
co
e A
lge
bra
1
Re
cog
niz
e A
rith
me
tic
Se
qu
en
ces
A s
eq
ue
nce
is
a s
et
of
nu
mbers
in
a s
peci
fic
ord
er.
If
the d
iffe
ren
ce b
etw
een
su
ccess
ive t
erm
s is
con
stan
t, t
hen
th
e s
equ
en
ce i
s ca
lled
an
a
rit
hm
eti
c s
eq
ue
nce
.
W
rit
e a
n e
qu
ati
on
fo
r
the
nth
te
rm
of
the
se
qu
en
ce
12
, 1
5,
18
, 2
1,
. .
. .
In t
his
sequ
en
ce, a
1 i
s 12. F
ind
th
e c
om
mon
d
iffe
ren
ce.
12
+ 3
+ 3
+ 3
15
18
21
Th
e c
om
mon
dif
fere
nce
is
3.
Use
th
e f
orm
ula
for
the n
th t
erm
to w
rite
an
equ
ati
on
.
a n =
a 1 +
(n
- 1
)d
Form
ula
for
the n
th t
erm
a n =
12
+ (
n -
1)3
a 1
= 1
2,
d =
3
a n =
12
+ 3
n -
3
Dis
trib
utive
Pro
pert
y
a n =
3n
+ 9
S
implif
y.
Th
e e
qu
ati
on
for
the n
th t
erm
is
a n =
3n
+ 9
.
Exerc
ises
De
term
ine
wh
eth
er e
ach
se
qu
en
ce
is a
n a
rit
hm
eti
c s
eq
ue
nce
. W
rit
e yes o
r no
.
Ex
pla
in.
1. 1, 5, 9, 13, 17, . . .
2. 8, 4, 0,
-4,
-8, . . .
3. 1, 3, 9, 27, 81, . . .
Fin
d t
he
ne
xt
thre
e t
erm
s o
f e
ach
arit
hm
eti
c s
eq
ue
nce
.
4. 9, 13, 17, 21, 25, . . .
5. 4, 0,
-4,
-8,
-12, . . .
6. 29, 35, 41, 47, . . .
Writ
e a
n e
qu
ati
on
fo
r t
he
nth
te
rm
of
ea
ch
arit
hm
eti
c s
eq
ue
nce
. T
he
n g
ra
ph
th
e
first
fiv
e t
erm
s o
f th
e s
eq
ue
nce
.
7. 1, 3, 5, 7, . . .
8.
-1,
-4,
-7,
-1
0, . . .
9.
-4,
-9,
-1
4,
-1
9, . . .
D
ete
rm
ine
wh
eth
er t
he
se
qu
en
ce
1,
3,
5,
7,
9,
11
, .
. .
is a
n
arit
hm
eti
c s
eq
ue
nce
. J
usti
fy y
ou
r
an
sw
er.
If p
oss
ible
, fi
nd
th
e c
om
mon
dif
fere
nce
betw
een
th
e t
erm
s. S
ince
3 -
1 =
2,
5 -
3 =
2, an
d s
o o
n, th
e c
om
mon
d
iffe
ren
ce i
s 2.
Sin
ce t
he d
iffe
ren
ce b
etw
een
th
e t
erm
s of
1, 3, 5, 7, 9, 11, . . . is
con
stan
t, t
his
is
an
ari
thm
eti
c se
qu
en
ce.
3-5
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Ari
thm
eti
c S
eq
uen
ces a
s L
inear
Fu
ncti
on
s
Ari
thm
eti
c S
eq
ue
nc
ea
nu
me
rica
l p
atte
rn t
ha
t in
cre
ase
s o
r d
ecre
ase
s a
t a
co
nsta
nt
rate
or
valu
e c
alle
d t
he
co
mm
on
dif
fere
nc
e
Te
rms
of
an
Ari
thm
eti
c S
eq
ue
nc
e If
a1 is t
he
! r
st
term
of
an
ari
thm
etic s
eq
ue
nce
with
co
mm
on
diff
ere
nce
d,
the
n t
he
se
qu
en
ce
is a
1,
a1 +
d,
a1 +
2d
, a
1 +
3d
, . . . .
nth
Te
rm o
f a
n A
rith
me
tic
Se
qu
en
ce
an =
a1 +
(n
- 1
)d
Exam
ple
1Exam
ple
2
2
9, 33, 37
-16,
-20,
-24
53, 59, 65
y
es;
d =
4
yes;
d =
-4
no
; n
o c
om
mo
n
dif
fere
nce
a
n =
2n
- 1
a
n =
-3n
+ 2
a
n =
-5n
+ 1
Lesson 3-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
31
G
len
co
e A
lge
bra
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Ari
thm
eti
c S
eq
uen
ces a
s L
inear
Fu
ncti
on
s
Ari
thm
eti
c S
eq
ue
nce
s a
nd
Fu
nct
ion
s A
n a
rit
hm
eti
c s
eq
ue
nce
is
a l
inear
fun
ctio
n i
n w
hic
h n
is
the i
nd
ep
en
den
t vari
able
, a
n i
s th
e d
ep
en
den
t vari
able
, an
d t
he
com
mon
dif
fere
nce
d i
s th
e s
lop
e. T
he f
orm
ula
can
be r
ew
ritt
en
as
the f
un
ctio
n
a n =
a 1 +
(n
- 1
)d, w
here
n i
s a c
ou
nti
ng n
um
ber.
S
EA
TIN
G T
he
re
are
20
se
ats
in
th
e f
irst
ro
w o
f th
e b
alc
on
y o
f th
e
au
dit
oriu
m. T
he
re
are
22
se
ats
in
th
e s
eco
nd
ro
w,
an
d 2
4 s
ea
ts i
n t
he
th
ird
ro
w.
a
. W
rit
e a
fu
ncti
on
to
re
pre
se
nt
this
se
qu
en
ce
.
Th
e f
irst
term
a 1 i
s 20. F
ind
th
e
com
mon
dif
fere
nce
.
20
+ 2
+ 2
22
24
T
he c
om
mon
dif
fere
nce
is
2.
a
n =
a 1 +
(n
- 1
)d
= 2
0 +
(n
- 1
)2
= 2
0 +
2n
- 2
= 1
8 +
2n
T
he f
un
ctio
n i
s a
n =
18 +
2n
.
b. G
ra
ph
th
e f
un
cti
on
.
Th
e r
ate
of
chan
ge i
s 2. M
ak
e a
table
an
d
plo
t p
oin
ts.
n a
n
12
0
22
2
32
4
42
6
nO
1
20
22
24
26
28
23
4
an
Exerc
ises
1
. K
NIT
TIN
G S
ara
h l
earn
s to
kn
it f
rom
her
gra
nd
moth
er.
Tw
o d
ays
ago, sh
e m
easu
red
th
e l
en
gth
of
the s
carf
sh
e i
s k
nit
tin
g t
o b
e 1
3 i
nch
es.
Yest
erd
ay,
sh
e m
easu
red
th
e
len
gth
of
the s
carf
to b
e 1
5.5
in
ches.
Tod
ay i
t m
easu
res
18 i
nch
es.
Wri
te a
fu
nct
ion
to r
ep
rese
nt
the a
rith
meti
c se
qu
en
ce.
2
. R
EFR
ES
HM
EN
TS
You
agre
e t
o p
ou
r w
ate
r in
to t
he c
up
s fo
r th
e
Boost
er
Clu
b a
t a f
ootb
all
gam
e. T
he p
itch
er
con
tain
s 64 o
un
ces
of
wate
r w
hen
you
begin
. A
fter
you
have f
ille
d 8
cu
ps,
th
e p
itch
er
is
em
pty
an
d m
ust
be r
efi
lled
.
a.
Wri
te a
fu
nct
ion
to r
ep
rese
nt
the a
rith
meti
c se
qu
en
ce.
an =
-8n
b.
Gra
ph
th
e f
un
ctio
n.
3-5
Form
ula
for
the n
th term
a 1 =
20 a
nd d
= 2
Dis
trib
utive
Pro
pert
y
Sim
plif
y.
an
nO
18
24
6
8
16
32
48
64
24
40
56
72
35
7
Exam
ple
an =
13 +
2.5
n
Answers (Lesson 3-5)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A15 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
32
G
len
co
e A
lge
bra
1
Sk
ills
Practi
ce
Ari
thm
eti
c S
eq
uen
ces a
s L
inear
Fu
ncti
on
s
De
term
ine
wh
eth
er e
ach
se
qu
en
ce
is a
n a
rit
hm
eti
c s
eq
ue
nce
. W
rit
e yes o
r no
.
Ex
pla
in.
1. 4, 7, 9, 12, . . .
2.
15, 13, 11, 9, . . .
3. 7, 10, 13, 16, . . .
4.
-6,
-5,
-3,
-1, . . .
5.
-5,
-3,
-1, 1, . . .
6.
-9,
-12,
-15,
-18, . . .
7. 10, 15, 25, 40, . . .
no
8.
-1
0,
-5,
0, 5, . . .
yes;
5
Fin
d t
he
ne
xt
thre
e t
erm
s o
f e
ach
arit
hm
eti
c s
eq
ue
nce
.
9. 3, 7, 11, 15, . . .
10. 22, 20, 18, 16, . . .
11.
-13,
-11,
-9,
-7 . . .
12.
-2,
-5,
-8,
-11, . . .
13. 19, 24, 29, 34, . . .
14. 16, 7,
-2,
-11, . . .
15. 2.5
, 5, 7.5
, 10, . . .
12.5
, 15, 17.
5
16. 3.1
, 4.1
, 5.1
, 6.1
, . . .
7.1, 8.1
, 9.1
Writ
e a
n e
qu
ati
on
fo
r t
he
nth
te
rm
of
ea
ch
arit
hm
eti
c s
eq
ue
nce
. T
he
n g
ra
ph
th
e
first
fiv
e t
erm
s o
f th
e s
eq
ue
nce
.
17. 7, 13, 19, 25, . . .
18. 30, 26, 22, 18, . . .
19.
-7,
-4,
-1, 2, . . .
20. V
IDE
O D
OW
NLO
AD
ING
Bri
an
is
dow
nlo
ad
ing e
pis
odes
of
his
favor
ite
TV
sh
ow t
o p
lay
on h
is p
erso
nal
med
ia d
evic
e. T
he
cost
to
dow
nlo
ad
1 e
pis
ode
is $
1.9
9. T
he
cost
to
dow
nlo
ad
2 e
pis
odes
is
$3.9
8. T
he
cost
to
dow
nlo
ad
3 e
pis
odes
is
$5.9
7. W
rite
a f
un
ctio
n
to r
epre
sen
t th
e ari
thm
etic
seq
uen
ce.
a
n =
1.9
9n
n
an
24
6
4
-4
-8O
n
an
O2
46
30
20
10
n
an
O2
46
30
20
10
3-5
no
yes; -
2
yes;
3n
o
yes;
2yes; -
3
-5, -
3, -
1-
14, -
17,
-20
39, 44, 49
-20, -
29, -
38
a
n =
6n
+ 1
a
n =
-4n
+ 3
4
a n =
3n
- 1
0
19, 23, 27
14, 12, 10
Lesson 3-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
33
G
len
co
e A
lge
bra
1
Practi
ce
Ari
thm
eti
c S
eq
uen
ces a
s L
inear
Fu
ncti
on
s
De
term
ine
wh
eth
er e
ach
se
qu
en
ce
is a
n a
rit
hm
eti
c s
eq
ue
nce
. W
rit
e yes o
r no
.
Ex
pla
in.
1. 21, 13, 5,
-3, . . .
2.
-5, 12, 29, 46, . . .
3.
-2.2
, -
1.1
, 0.1
, 1.3
, . . .
4. 1, 4, 9, 16, . . .
5. 9, 16, 23, 30, . . .
6.
-1.2
, 0.6
, 1.8
, 3.0
, . . .
Fin
d t
he
ne
xt
thre
e t
erm
s o
f e
ach
arit
hm
eti
c s
eq
ue
nce
.
7. 82, 76, 70, 64, . . .
8.
-49,
-35,
-21,
-7, . . .
9. 3
−
4 ,
1
−
2 ,
1
−
4 ,
0, . . .
10.
-10,
-3, 4, 11 . . .
11. 12, 10, 8, 6, . . .
12. 12, 7, 2,
-3, . . .
Writ
e a
n e
qu
ati
on
fo
r t
he
nth
te
rm
of
ea
ch
arit
hm
eti
c s
eq
ue
nce
. T
he
n g
ra
ph
th
e
first
fiv
e t
erm
s o
f th
e s
eq
ue
nce
.
13. 9, 13, 17, 21, . . .
14.
-5,
-2, 1, 4, . . .
15. 19, 31, 43, 55, . . .
16. B
AN
KIN
G C
hem
dep
osit
ed $
115.0
0 i
n a
savin
gs
acc
oun
t. E
ach
wee
k t
her
eaft
er, h
e d
epos
its
$35.0
0 i
nto
th
e acc
oun
t.
a.
Wri
te a
fu
nct
ion
to
rep
rese
nt
the
tota
l am
oun
t C
hem
has
dep
osit
ed f
or a
ny p
art
icu
lar
nu
mber
of
wee
ks
aft
er h
is i
nit
ial
dep
osit
.
b.
How
mu
ch h
as
Ch
em d
epos
ited
30 w
eek
s aft
er h
is i
nit
ial
dep
osit
?
17. S
TO
RE
DIS
PLA
YS
Tam
ika i
s st
ack
ing b
oxes
of
tiss
ue
for
a s
tore
dis
pla
y. E
ach
row
of
tiss
ues
has
2 f
ewer
box
es t
han
th
e ro
w b
elow
. T
he
firs
t ro
w h
as
23 b
oxes
of
tiss
ues
.
a.
Wri
te a
fu
nct
ion
to
rep
rese
nt
the
ari
thm
etic
seq
uen
ce.
b.
How
man
y b
oxes
wil
l th
ere
be
in t
he
ten
th r
ow?
n
an
O60
40
20
24
6
n
an
24
6
8 4
-4O
n
an
O2
46
30
20
10
3-5
y
es;
d =
-8
yes;
d =
17
no
; n
o c
om
mo
n
dif
fere
nce
5
8, 52, 46
7, 21, 35
- 1
−
4 ,
- 1
−
2 ,
- 3
−
4
a
n =
4n
+ 5
a
n =
3n
- 8
a
n =
12n
+ 7
a n =
35n
+ 1
15
$11
65
5
1
8, 25, 32
4, 2, 0
-8,
-13,
-18
a n =
-2n
+ 2
5
n
o;
no
co
mm
on
y
es;
d =
7
no
; n
o c
om
mo
n
dif
fere
nce
d
iffe
ren
ce
Answers (Lesson 3-5)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A16 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
34
G
len
co
e A
lge
bra
1
1.P
OS
TA
GE
Th
e p
rice
to
sen
d a
larg
e en
vel
ope
firs
t cl
ass
is
88 c
ents
for
th
e fi
rst
oun
ce a
nd
17 c
ents
for
each
ad
dit
ion
al
oun
ce. T
he
table
bel
ow s
how
s th
e co
st f
or w
eigh
ts u
p t
o5
oun
ces.
So
urc
e:
United S
tate
s P
osta
l S
erv
cie
H
ow m
uch
did
a l
arg
e en
vel
ope
wei
gh
th
at
cost
$2.0
7 t
o se
nd
?
2. S
PO
RT
S W
an
da i
s th
e m
an
ager
for
th
e so
ccer
tea
m. O
ne
of h
er d
uti
es i
s to
han
d
out
cup
s of
wate
r at
pra
ctic
e. E
ach
cu
p o
f w
ate
r is
4 o
un
ces.
Sh
e beg
ins
pra
ctic
e w
ith
a 1
28-o
un
ce c
oole
r of
wate
r. H
ow
mu
ch w
ate
r is
rem
ain
ing a
fter
sh
e h
an
ds
out
the
14th
cu
p?
3. T
HE
AT
ER
A t
hea
ter
has
20 s
eats
in
th
e fi
rst
row
, 22 i
n t
he
seco
nd
row
, 24 i
n t
he
thir
d r
ow, an
d s
o on
for
25 r
ows.
How
m
an
y s
eats
are
in
th
e la
st r
ow?
4.N
UM
BE
R T
HE
OR
Y O
ne
of t
he
mos
t fa
mou
s se
qu
ence
s in
math
emati
cs i
s th
e F
ibon
acc
i se
qu
ence
. It
is
nam
ed a
fter
L
eon
ard
o d
e P
isa (
1170–1250)
or F
iliu
s B
onacc
i, a
lias
Leo
nard
o F
ibon
acc
i. T
he
firs
t se
ver
al
nu
mber
s in
th
e F
ibon
acc
i se
qu
ence
are
:1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, . . .
Doe
s th
is r
epre
sen
t an
ari
thm
etic
se
qu
ence
? W
hy o
r w
hy n
ot?
5
. S
AV
ING
S I
nga’s
gra
nd
fath
er d
ecid
es t
o st
art
a f
un
d f
or h
er c
olle
ge
edu
cati
on. H
e m
ak
es a
n i
nit
ial
con
trib
uti
on o
f $3000
an
d e
ach
mon
th d
epos
its
an
ad
dit
ion
al
$500. A
fter
on
e m
onth
he
wil
l h
ave
con
trib
ute
d $
3500.
a.
Wri
te a
n e
qu
ati
on f
or t
he
nth
ter
m o
f th
e se
qu
ence
.
b.
How
mu
ch m
oney
wil
l In
ga’s
gra
nd
fath
er h
ave
con
trib
ute
d a
fter
24 m
onth
s?
$15,0
00
Wo
rd P
rob
lem
Pra
ctic
eA
rith
meti
c S
eq
uen
ces a
s L
inear
Fu
ncti
on
s
3-5 W
eig
ht
(ou
nc
es
)1
23
45
Po
sta
ge
(do
lla
rs)
0.8
81.
05
1.2
21.
39
1.5
6
8 o
un
ces
72 o
un
ces
68 s
eats
No
, b
ecau
se t
he d
iffe
ren
ce
betw
een
term
s i
s n
ot
co
nsta
nt.
an =
30
00
+ 5
00n
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 3-5
Ch
ap
ter
3
35
G
len
co
e A
lge
bra
1
Ari
thm
eti
c S
eri
es
An
ari
thm
etic
ser
ies
is a
ser
ies
in w
hic
h e
ach
ter
m a
fter
th
e fi
rst
may b
e fo
un
d b
y a
dd
ing t
he
sam
e n
um
ber
to
the
pre
ced
ing t
erm
. L
et S
sta
nd
for
th
e fo
llow
ing s
erie
s in
wh
ich
each
ter
m
is 3
mor
e th
an
th
e p
rece
din
g o
ne.
S =
2 +
5 +
8 +
11
+ 1
4 +
17
+ 2
0
Th
e se
ries
rem
ain
s th
e sa
me
if w
e
S =
2
+
5 +
8
+ 1
1 +
14
+ 1
7 +
20
rever
se t
he
ord
er o
f all
th
e te
rms.
So
S
= 2
0 +
17
+ 1
4 +
11
+
8 +
5
+
2
let
us
rever
se t
he
ord
er o
f th
e te
rms
2
S =
22
+ 2
2 +
22
+ 2
2 +
22
+ 2
2 +
22
an
d a
dd
on
e se
ries
to
the
oth
er, te
rm
2S
= 7
(22)
by t
erm
. T
his
is
show
n a
t th
e ri
gh
t.
S =
7(2
2)
−
2
=
7(1
1)
= 7
7L
et a
rep
rese
nt
the
firs
t te
rm o
f th
e se
ries
.
Let
ℓ r
epre
sen
t th
e la
st t
erm
of
the
seri
es.
Let
n r
epre
sen
t th
e n
um
ber
of
term
s in
th
e se
ries
.
In t
he
pre
ced
ing e
xam
ple
, a
= 2
, ℓ =
20, an
d n
= 7
. N
otic
e th
at
wh
en y
ou a
dd
th
e tw
o se
ries
, te
rm b
y t
erm
, th
e su
m o
f ea
ch p
air
of
term
s is
22. T
hat
sum
can
be
fou
nd
by a
dd
ing t
he
firs
t an
d l
ast
ter
ms,
2 +
20 o
r a
+ ℓ
. N
otic
e als
o th
at
ther
e are
7, or
n, su
ch s
um
s. T
her
efor
e, t
he
valu
e of
2S
is
7(2
2),
or
n(a
+ ℓ
) in
th
e gen
eral
case
. S
ince
th
is i
s tw
ice
the
sum
of t
he
seri
es, you
can
use
th
e fo
rmu
la
S =
n
(a +
ℓ)
−
2
to
fin
d t
he
sum
of
an
y a
rith
met
ic s
erie
s.
F
ind
th
e s
um
: 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
.
a =
1,
ℓ =
9, n
= 9
, so
S =
9(1
+ 9
) −
2
= 9 . 1
0
−
2
= 4
5
F
ind
th
e s
um
: -
9 +
(-
5)
+ (
-1
) +
3 +
7 +
11
+ 1
5.
a =
29,
ℓ =
15, n
= 7
, so
S =
7(-
9 +
15)
−
2
= 7
.6
−
2 =
21
Exerc
ises
Fin
d t
he
su
m o
f e
ach
arit
hm
eti
c s
erie
s.
1.
3 +
6 +
9 +
12
+ 1
5 +
18
+ 2
1 +
24
2. 10
+ 1
5 +
20
+ 2
5 +
30
+ 3
5 +
40
+ 4
5 +
50
3.
-21
+ (
-16)
+ (
-11)
+ (
-6)
+ (
-1)
+ 4
+ 9
+ 1
4
4. ev
en w
hol
e n
um
ber
s fr
om 2
th
rou
gh
100
5. od
d w
hol
e n
um
ber
s bet
wee
n 0
an
d 1
00
En
ric
hm
en
t 3
-5
Exam
ple
1
Exam
ple
2
108
270
-28
2550
250
0
Answers (Lesson 3-5)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A17 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
36
G
len
co
e A
lge
bra
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n
Pro
po
rtio
nal
an
d N
on
pro
po
rtio
nal
Rela
tio
nsh
ips
Pro
po
rtio
na
l R
ela
tio
nsh
ips
If t
he r
ela
tion
ship
betw
een
th
e d
om
ain
an
d r
an
ge o
f a
rela
tion
is
lin
ear,
th
e r
ela
tion
ship
can
be d
esc
ribed
by a
lin
ear
equ
ati
on
. If
th
e e
qu
ati
on
p
ass
es
thro
ugh
(0, 0)
an
d i
s of
the f
orm
y =
kx, th
en
th
e r
ela
tion
ship
is
pro
port
ion
al.
CO
MPA
CT
DIS
CS
S
up
po
se
yo
u p
urch
ase
d a
nu
mb
er o
f p
ack
ag
es o
f
bla
nk
co
mp
act
dis
cs.
If e
ach
pa
ck
ag
e c
on
tain
s 3
co
mp
act
dis
cs,
yo
u c
ou
ld m
ak
e a
ch
art
to s
ho
w t
he
re
lati
on
sh
ip b
etw
ee
n t
he
nu
mb
er o
f p
ack
ag
es o
f co
mp
act
dis
cs
an
d t
he
nu
mb
er o
f d
iscs p
urch
ase
d.
Use
x f
or t
he
nu
mb
er o
f p
ack
ag
es a
nd
y f
or t
he
nu
mb
er o
f co
mp
act
dis
cs.
Mak
e a
table
of
ord
ere
d p
air
s fo
r se
vera
l p
oin
ts o
f th
e g
rap
h.
N
um
be
r o
f P
ack
ag
es
12
34
5
Nu
mb
er
of
CD
s3
69
12
15
Th
e d
iffe
ren
ce i
n t
he x
valu
es
is 1
, an
d t
he d
iffe
ren
ce i
n t
he y
valu
es
is 3
. T
his
patt
ern
sh
ow
s th
at
y i
s alw
ays
thre
e t
imes
x. T
his
su
ggest
s th
e r
ela
tion
y =
3x. S
ince
th
e r
ela
tion
is
als
o a
fu
nct
ion
, w
e c
an
wri
te t
he e
qu
ati
on
in
fu
nct
ion
nota
tion
as
f(x)
= 3
x.
Th
e r
ela
tion
in
clu
des
the p
oin
t (0
, 0)
beca
use
if
you
bu
y 0
pack
ages
of
com
pact
dis
cs, you
w
ill
not
have a
ny c
om
pact
dis
cs. T
here
fore
, th
e r
ela
tion
ship
is
pro
port
ion
al.
Exerc
ises
1
. N
AT
UR
AL G
AS
N
atu
ral
gas
use
is
oft
en
measu
red
in
“th
erm
s.”
Th
e t
ota
l am
ou
nt
a g
as
com
pan
y w
ill
charg
e f
or
natu
ral
gas
use
is
base
d o
n h
ow
mu
ch n
atu
ral
gas
a h
ou
seh
old
u
ses.
Th
e t
able
sh
ow
s th
e r
ela
tion
ship
betw
een
natu
ral
gas
use
an
d t
he t
ota
l co
st.
Ga
s U
se
d (
the
rms
)1
23
4
To
tal
Co
st
($)
$1.
30
$2
.60
$3
.90
$5
.20
a.
Gra
ph
th
e d
ata
. W
hat
can
you
ded
uce
fro
m t
he p
att
ern
abou
t th
e r
ela
tion
ship
betw
een
th
e n
um
ber
of
therm
s u
sed
an
d t
he t
ota
l co
st?
Th
e r
ela
tio
nsh
ip i
s p
rop
ort
ion
al.
b.
Wri
te a
n e
qu
ati
on
to d
esc
ribe t
his
rela
tion
ship
. y =
1.3
0x
c.
Use
th
is e
qu
ati
on
to p
red
ict
how
mu
ch i
t w
ill
cost
if
a h
ou
seh
old
u
ses
40 t
herm
s.
$52.0
0
3-6 Exam
ple
Total Cost ($)
23 1
0
456y
Gas
Use
d (
ther
ms)
32
1x
4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 3-6
Ch
ap
ter
3
37
G
len
co
e A
lge
bra
1
Stu
dy
Gu
ide a
nd
In
terv
en
tio
n (c
on
tin
ued
)
Pro
po
rtio
nal
an
d N
on
pro
po
rtio
nal
Rela
tio
nsh
ips
No
np
rop
ort
ion
al
Re
lati
on
ship
s If
th
e r
ati
o o
f th
e v
alu
e o
f x t
o t
he v
alu
e o
f y i
s d
iffe
ren
t fo
r se
lect
ord
ere
d p
air
s on
th
e l
ine, th
e e
qu
ati
on
is
non
pro
port
ion
al.
W
rit
e a
n e
qu
ati
on
in
fu
ncti
on
al
no
tati
on
fo
r t
he
re
lati
on
sh
ow
n
in t
he
gra
ph
.
Sele
ct p
oin
ts f
rom
th
e g
rap
h a
nd
pla
ce t
hem
in
a t
able
.
x
-1
01
23
y4
20
-2
-4
y
x
Th
e d
iffe
ren
ce b
etw
een
th
e x
–valu
es
is 1
, w
hil
e t
he
dif
fere
nce
betw
een
th
e y
-valu
es
is –
2. T
his
su
ggest
s th
at
y =
–2
x.
If x
= 1
, th
en
y =
–2(1
) or
–2. B
ut
the y
–valu
e f
or
x =
1 i
s 0.
x
1
2
3
-2
x-
2-
4-
6
y
0-
2-
4
y is a
lways
2 m
ore
than -
2x
Th
is p
att
ern
sh
ow
s th
at
2 s
hou
ld b
e a
dd
ed
to o
ne s
ide o
f th
e e
qu
ati
on
. T
hu
s, t
he e
qu
ati
on
is
y =
-2
x +
2.
Exerc
ises
Writ
e a
n e
qu
ati
on
in
fu
ncti
on
no
tati
on
fo
r t
he
re
lati
on
sh
ow
n i
n
the
ta
ble
. T
he
n c
om
ple
te t
he
ta
ble
.
1
. x
-1
01
23
4
y-
22
610
14
18
2
. x
-2
-1
01
23
y10
7
4 1
-2
-5
Writ
e a
n e
qu
ati
on
in
fu
ncti
on
no
tati
on
fo
r e
ach
re
lati
on
.
3
.
x
y
O
4.
x
y O
3-6 Exam
ple
f(x
) =
4x
+ 2
f(x
) =
-3x
+ 4
f(x
) =
-x
+ 2
f
(x)
= 2
x +
2
Answers (Lesson 3-6)
Co
pyrig
ht ©
Gle
nc
oe
/Mc
Gra
w-H
ill, a d
ivis
ion
of T
he M
cG
raw
-Hill C
om
pan
ies, In
c.
Chapter 3 A18 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
38
G
len
co
e A
lge
bra
1
Sk
ills
Practi
ce
Pro
po
rtio
nal
an
d N
on
pro
po
rtio
nal
Rela
tio
nsh
ips
Writ
e a
n e
qu
ati
on
in
fu
ncti
on
no
tati
on
fo
r e
ach
re
lati
on
.
1.
2.
3.
4.
5.
6.
7
. G
AM
ESH
OW
S T
he t
able
sh
ow
s h
ow
man
y p
oin
ts a
re a
ward
ed
for
an
sweri
ng
con
secu
tive q
uest
ion
s on
a g
am
esh
ow
.
Qu
es
tio
n a
nsw
ere
d1
23
45
Po
ints
aw
ard
ed
20
04
00
60
08
00
10
00
a
. W
rite
an
equ
ati
on
for
the d
ata
giv
en
. y =
20
0x
b
. F
ind
th
e n
um
ber
of
poin
ts a
ward
ed
if
9 q
uest
ion
s w
ere
an
swere
d.
180
0
xO
f(x)
xO
f(x)
xO
f(x)
xO
f(x)
xO
f(x)
xO
f(x)
3-6
f
(x)
= -
2x
f(x
) =
x -
2
f
(x)
= 1
- x
f(x
) =
x +
6
f
(x)
= 5
- x
f(x
) =
2x
- 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 3-6
Ch
ap
ter
3
39
G
len
co
e A
lge
bra
1
Practi
ce
Pro
po
rtio
nal
an
d N
on
pro
po
rtio
nal
Rela
tio
nsh
ips
1.B
IOLO
GY
M
ale
fir
efl
ies
flash
in
vari
ou
s p
att
ern
s to
sig
nal
loca
tion
an
d p
erh
ap
s to
ward
off
pre
dato
rs. D
iffe
ren
t sp
eci
es
of
fire
flie
s h
ave d
iffe
ren
t fl
ash
ch
ara
cteri
stic
s, s
uch
as
the
inte
nsi
ty o
f th
e f
lash
, it
s ra
te, an
d i
ts s
hap
e. T
he t
able
belo
w s
how
s th
e r
ate
at
wh
ich
a
male
fir
efl
y i
s fl
ash
ing.
Tim
es
(s
ec
on
ds
)1
23
4 5
Nu
mb
er
of
Fla
sh
es
24
68
10
a.
Wri
te a
n e
qu
ati
on
in
fu
nct
ion
nota
tion
for
the r
ela
tion
.
b.
How
man
y t
imes
wil
l th
e f
irefl
y f
lash
in
20 s
eco
nd
s?
2. G
EO
ME
TR
Y T
he t
able
sh
ow
s th
e n
um
ber
of
dia
gon
als
that
can
be d
raw
n f
rom
on
e v
ert
ex i
n a
poly
gon
. W
rite
an
equ
ati
on
in
fu
nct
ion
nota
tion
for
the r
ela
tion
an
d
fin
d t
he n
um
ber
of
dia
gon
als
th
at
can
be d
raw
n f
rom
on
e v
ert
ex i
n a
12-s
ided
poly
gon
.
Writ
e a
n e
qu
ati
on
in
fu
ncti
on
no
tati
on
fo
r e
ach
re
lati
on
.
3.
4.
5.
Fo
r e
ach
arit
hm
eti
c s
eq
ue
nce
, d
ete
rm
ine
th
e r
ela
ted
fu
ncti
on
. T
he
n d
ete
rm
ine
if t
he
fu
ncti
on
is p
ro
po
rti
on
al
or n
on
pro
po
rti
on
al.
Ex
pla
in.
6. 1, 3, 5, . . .
7. 2, 7, 12, . . .
8.
-3,
-6,
-9, . . .
a(n
) =
2n
- 1
; a
(n)
= 5
n-
3;
a
(n)
=-
3n
;
n
on
pro
po
rtio
nal;
n
on
pro
po
rtio
nal;
p
rop
ort
ion
al;
n
ot
of
form
y=
kx
no
t o
f fo
rm y
=kx
of
form
y=
kx
x
y O
x
y
O
x
y
O
3-6
Sid
es
34
56
Dia
go
na
ls0
12
3
f
(x)
= -
1
−
2 x
f
(x)
= 3
x -
6
f(x
) =
2x
+ 4
f(t)
= 2
t, w
here
t i
s t
he
40
f(s)
= s
- 3
, w
here
s i
s t
he n
um
ber
of
sid
es
tim
e i
n s
eco
nd
s a
nd
f(t
) is
th
e n
um
ber
of
! ash
es
an
d f
(s)
is t
he n
um
ber
of
dia
go
nals
; 9
Answers (Lesson 3-6)
Answers
Co
pyri
gh
t ©
Gle
nco
e/M
cG
raw
-Hill, a
div
isio
n o
f T
he
Mc
Gra
w-H
ill C
om
pa
nie
s,
Inc
.
Chapter 3 A19 Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Ch
ap
ter
3
40
G
len
co
e A
lge
bra
1
Wo
rd
Pro
ble
m P
racti
ce
Pro
po
rtio
nal
an
d N
on
pro
po
rtio
nal
Rela
tio
nsh
ips
1.O
NLIN
E S
HO
PP
ING
Ric
ard
o is
bu
yin
g
com
pu
ter
cable
s fr
om a
n o
nli
ne
stor
e. I
f h
e bu
ys
4 c
able
s, t
he
tota
l co
st w
ill
be
$24. If
he
bu
ys
5 c
able
s, t
he
tota
l co
st
wil
l be
$29. If
th
e to
tal
cost
can
be
rep
rese
nte
d b
y a
lin
ear
fun
ctio
n, w
ill
the
fun
ctio
n b
e p
rop
ort
ion
al
or
non
pro
port
ion
al?
Exp
lain
.
2. FO
OD
It
tak
es a
bou
t fo
ur
pou
nd
s of
gra
pes
to
pro
du
ce o
ne
pou
nd
of
rais
ins.
T
he
gra
ph
sh
ows
the
rela
tion
for
th
e n
um
ber
of
pou
nd
s of
gra
pes
nee
ded
, x,
to m
ak
e y p
oun
ds
of r
ais
ins.
Wri
te a
n
equ
ati
on i
n f
un
ctio
n n
otati
on f
or t
he
rela
tion
sh
own
.
3. PA
RK
ING
Palm
er T
own
ship
rec
entl
y
inst
all
ed p
ark
ing m
eter
s in
th
eir
mu
nic
ipal
lot.
Th
e co
st t
o p
ark
for
h
hou
rs i
s re
pre
sen
ted
by t
he
equ
ati
on
C =
0.2
5h
.
a
. M
ak
e a t
able
of
valu
es t
hat
rep
rese
nts
th
is r
elati
onsh
ip.
b. D
escr
ibe
the
rela
tion
ship
bet
wee
n t
he
tim
e p
ark
ed a
nd
th
e co
st.
4.M
US
IC A
mea
sure
of
mu
sic
con
tain
s th
e sa
me
nu
mber
of
bea
ts t
hro
ugh
out
the
son
g. T
he
table
sh
ows
the
rela
tion
for
th
e n
um
ber
of
bea
ts c
oun
ted
aft
er a
cer
tain
n
um
ber
of
mea
sure
s h
ave
bee
n p
layed
in
th
e si
x-e
igh
t ti
me.
Wri
te a
n e
qu
ati
on t
o d
escr
ibe
this
rel
ati
onsh
ip.
So
urce:
Sheet
Music
USA
5. G
EO
ME
TR
Y A
fra
ctal
is a
patt
ern
co
nta
inin
g p
art
s w
hic
h a
re i
den
tica
l to
th
e ov
erall
patt
ern
. T
he
foll
owin
g
geo
met
ric
patt
ern
is
a f
ract
al.
a.
Com
ple
te t
he
table
.
b.
Wh
at
are
th
e n
ext
thre
e n
um
ber
s in
th
e p
att
ern
?
c.
Wri
te a
n e
qu
ati
on i
n f
un
ctio
n n
otati
on
for
the
patt
ern
.
Po
un
ds
of
Gra
pes
21
04
3
f(
x)
x5
67
8
Pounds of Raisins
1.5
2.0
1.0
0.5
2.5
4.0
3.5
3.0
3-6
Me
as
ure
s
Pla
ye
d (
x)
12
34
56
To
tal
Nu
mb
er
of
Be
ats
(y)
612
18
24
30
36
Te
rmx
12
34
Nu
mb
er
of
Sm
all
er
Tri
an
gle
s
y1
4
9
16
y
= 6
x
25, 36, 49
f(x)
= x
2
no
np
rop
ort
ion
al;
do
es n
ot
pass t
hro
ug
h (
0, 0)
f
(x)
= 0
.25x
It c
osts
25 c
en
ts f
or
each
h
ou
r yo
u p
ark
in
th
e l
ot.
Tim
eh
12
34
Co
st
C0
.25
0.5
0.7
51.
0
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
DA
TE
PE
RIO
D
Lesson 3-6
Ch
ap
ter
3
41
G
len
co
e A
lge
bra
1
En
ric
hm
en
t
Taxic
ab
Gra
ph
sY
ou h
ave
use
d a
rec
tan
gu
lar
coor
din
ate
syst
em t
o gra
ph
x
y
O
y =
x -
1
y =
-2
equ
ati
ons
such
as
y =
x -
1 o
n a
coo
rdin
ate
pla
ne.
In
a
coor
din
ate
pla
ne,
th
e n
um
ber
s in
an
ord
ered
pair
(x, y)
can
be
an
y t
wo
real
nu
mber
s.
A t
ax
ica
b p
lan
e i
s d
iffe
ren
t fr
om t
he
usu
al
coor
din
ate
pla
ne.
T
he
only
poi
nts
all
owed
are
th
ose
that
exis
t alo
ng t
he
hor
izon
tal
an
d v
erti
cal
gri
d l
ines
. Y
ou m
ay t
hin
k o
f th
e p
oin
ts
as
taxic
abs
that
mu
st s
tay o
n t
he
stre
ets.
Th
e ta
xic
ab g
rap
h s
how
s th
e eq
uati
ons
y =
-2 a
nd
y =
x -
1.
Not
ice
that
one
of t
he
gra
ph
s is
no
lon
ger
a s
traig
ht
lin
e. I
t is
n
ow a
col
lect
ion
of
sep
ara
te p
oin
ts.
Gra
ph
th
ese
eq
ua
tio
ns o
n t
he
ta
xic
ab
pla
ne
at
the
rig
ht.
x
y
O
1.
1.
2.
2.
3.
3.
4.
4.
1. y
= x
+ 1
2. y
= -
2x
+ 3
3. y
= 2
.5
4. x
= -
4
Use
yo
ur g
ra
ph
s f
or t
he
se
pro
ble
ms.
5. W
hic
h o
f th
e eq
uati
ons
has
the
sam
e gra
ph
in
bot
h t
he
usu
al
coor
din
ate
pla
ne
an
d t
he
taxic
ab p
lan
e?
6. D
escr
ibe
the
form
of
equ
ati
ons
that
have
the
sam
e gra
ph
in
bot
h t
he
usu
al
coor
din
ate
pla
ne
an
d t
he
taxic
ab p
lan
e.
In t
he
ta
xic
ab
pla
ne
, d
ista
nce
s a
re
no
t m
ea
su
re
d d
iag
on
all
y,
bu
t a
lon
g t
he
str
ee
ts.
Writ
e t
he
ta
xi-
dis
tan
ce
be
twe
en
ea
ch
pa
ir o
f p
oin
ts.
7. (0
, 0)
an
d (
5, 2)
8. (0
, 0)
an
d (
-3, 2)
9. (0
, 0)
an
d (
2, 1.5
)
10. (1
, 2)
an
d (
4, 3)
11. (2
, 4)
an
d (
-1, 3)
12. (0
, 4)
an
d (
-2, 0)
Dra
w t
he
se
gra
ph
s o
n t
he
ta
xic
ab
grid
at
the
rig
ht.
13. T
he
set
of p
oin
ts w
hos
e ta
xi-
dis
tan
ce f
rom
(0, 0)
is 2
un
its.
14. T
he
set
of p
oin
ts w
hos
e ta
xi-
dis
tan
ce f
rom
(2, 1)
is 3
un
its.
x
y
O
3-6
x =
-4
x =
A a
nd
y =
B, w
here
A a
nd
B a
re i
nte
gers
7 u
nit
s
5 u
nit
s
3.5
un
its
4 u
nit
s
4 u
nit
s
6 u
nit
s
ind
icate
d b
y ×
ind
icate
d b
y d
ots
Answers (Lesson 3-6)
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