13.7 – Writing Linear Equations y=mx+b What does the m represent? What does the b represent? Name the slope and y- intercept of each line m b BLUE GREEN PURPLE 5 1 2 3 2 1 2 0 2 SLOPE!!! Y-INT!!! Y
Jan 08, 2016
13.7 – Writing Linear Equations
y=mx+b What does the m represent?
What does the b represent?
Name the slope and y-intercept of each line
m b
BLUE
GREEN
PURPLE
5
1
2
3
2
1
2
0
2
SLOPE!!! Y-INT!!!
Y
We are going to learn how to write equations.
There are three main types.
1) Slope and y-intercept
2) Slope and a point
3) Two points
12 :int-y5
2- :slope
: whenline theofequation an Write
5
2-
12 xy m b
4
1- :int-y
2
1 :slope
: whenline theofequation an Write
2
1
xy m b
1 :int-y
0 :slope
: whenline theofequation an Write
0 xy m b
1
4
1-
line. thisofequation theWrite
Y - I N T = 3
m = 1
y = 1 x + 3
Solve for y, change it to ‘y =‘
)1(32 xy
Distribute
Get y by itself
332 xy22 13 xy
)62(3
27 xy
43
47 xy
77
113
4 xy
We are going to learn how to write equations.
There are three main types.
1) Slope and y-intercept
2) Slope and a point
3) Two points
Slope-intercept formPoint-slope form
bmxy )( 11 xxmyy Plug in the slope and the point into point slope form
Writing an equation given a slope and a point.
Solve for y (get y by itself)
Plug in the slope and the point into point slope form
3
2m (-6,1)
11 yx)( 11 xxmyy 1 –6 2
3
43
21 xy
11
53
2 xy
Slope-intercept form
Point-slope form
bmxy )( 11 xxmyy
Write the equation of the line given a point and a slope in point-slope form
2
1m (4,2)
11 yx)( 11 xxmyy 2 41
2
Standard form CByAx
Slope-intercept form
Point-slope form
bmxy )( 11 xxmyy
Write the equation of the line given a point and a slope in SLOPE-INTERCEPT FORM
2
1m (4,2)
11 yx)( 11 xxmyy 2 41
2
22
12 xy
22
xy2
1
Standard form CByAx
SLOPE = m =y2 – y1
x2 – x1
Find points and label
Plug into formula
Reduce Fraction
(3,-1) (2, 3)
x1 y1 x2 y2
x2 x1
y1y2
2 3
-13
4-1
Find points and label
Plug into formula
Reduce Fraction
(0, 2) (2, -4)
x1 y1 x2 y2
x2 x1
y1y2
2 0
2-4
-62
4 3
We are going to learn how to write equations.
There are three main types.
1) Slope and y-intercept
2) Slope and a point
3) Two points
One new thing:
Find your own darn slope!
ADJ:AJDSAK:JFDS:FJIJOWEJC:DSJK:FJKOWEIJFKSD:EJIFLSJFKSLFJSKFLJSFELIWPOWPJDPWAOJLJFSLSDEFPWOPEFJSLKFJWPEJFSDLFJSLOPEDSJFKL:WJPAFJPDSVOJDSPKFEIWLPJFKLSDFJ:AJWPVDSNFELWKGJWLEGIJLRIJGDFI
Slope-intercept form
Point-slope form
bmxy )( 11 xxmyy
1) Find slope
2) Take slope, ANY POINT
3) Change into correct form
m =y2 – y1
x2 – x1
(3,-1) (2, 3)
x1 y1 x2 y2 x2 x1
y1y2
2 3
-13
4-1
4
)( 11 xxmyy 3 2 -4
843 xy33 114 xy
Standard form CByAx
Slope-int
Slope-intercept form
Point-slope form
bmxy )( 11 xxmyy
1) Find slope
2) Take slope, ANY POINT
3) Change into correct form
m =y2 – y1
x2 – x1
(-4,1) (6, -4)
x1 y1 x2 y2x2 x1
y1y2
6 -4
1-4
-510
2
1
)( 11 xxmyy 1 –4 -12
22
11 xy
11
12
1 xy
Standard form CByAx
Slope-int
Slope-intercept form
Point-slope form
bmxy )( 11 xxmyy
1) Find slope
2) Take slope, ANY POINT
3) Change into correct form
m =y2 – y1
x2 – x1
(0,5) (6, 7)
x1 y1 x2 y2x2 x1
y1y2
6 0
57
26
3
1
)( 11 xxmyy 5 0 13
xy3
15 )(3
xy 153
Standard form CByAx
Standard yx 315
• Practice problems
Slope – Int Standard
(3, 4); (1, 2) (-2, 4) (1, -5)
• HW #55: Pg 555: 8, 10, 17 – 20 (slope-int and standard) 22, 23, 25 – 30 (even standard, odd slope-intercept), 33 – 38. (20 problems, end problems not easy)– Hint for 33, think circumcenter.