More Easy Graph Formulas

8/14/2019 More Easy Graph Formulas

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More Easy Graph Formulas


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TODAYS LESSON:

Slope-Intercept Form

Point-Slope Form

Standard Form


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Every line

has a

formulathat

describes

it!

For every

X, there isa Y!

(2,3)

(-2,0)


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Even if a

point

isnt

exactly

on a

line, it

still hasanX& Y(-1.5434,1.43423)

(5.45, 7.8)


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Question: How many exact points

are there on a line?

I give

hint:More

than

one

Answer:


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Remember

when y is by

itself:

y = 4x + 5

y-intercept = 5

SLOPE


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This Y by itself form is officially called

SLOPE-INTERCEPT FORMSLOPE-INTERCEPT FORM

...because it tells you the SLOPE& the Y-

Interceptof the line..

y = mx + bwhere the m is the slopeand the b is the y-intercept


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Guess what? You can find the Y-

intercept from ANY two points!

WITH

ALGEBRA!!!


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y = mx + b

Example: Write the formula for a function that

passes through (1,8) & (2,10).

STEP 1:Wecan find the

slope

with the two

points!!

8 101 2

= -2-1

=

y = m x + b

2


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Example: Write the formula for a function

that passes through (1,8) & (2,10).

y = 2x + bStep 2: Pick oneof the points

given, &

plug them in

for x & y !

Does it

matter

which

one??

Nope!Both points

are part of

the formula!

So either

one works!

8= 2(1) + b


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Example: Write the formula for a function

that passes through (1,8) & (2,10).

8= 2(1) + bSTEP 3: Solve forb (to find the

y-intercept) 8 = 2 + b-2-2

6 = bSTEP 4: Write the

formula !

y = mx+ b2 6


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Write a formula that passes through

the points (4,5) and (12,-5)

1) Find Slope2) Find the

Y-Intercept by

plugging in the Slopeand the X & Y of one

of the points.

3) Re-write theformula with the Slope

and Y-intercept

plugged in.

Fi d th f l f f ti th t


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Find the formula of a function that

passes through these points:

(9,-3) and (-3,-3)1) Slope is

2) Y Intercept is

3) Formula!


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In addition to the Slope-Intersect Form

y = mx + b

there is another form called the Point-

Slope Form


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Point-Slope FormFor this type of formula, you only need to

know any point, and the slope!

y y1 = m(x x1)

What this??Trog no like

little numbers!!


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EXAMPLE: A point on a line is

(4,6). The slope is . Writethe formula.

y y1 = m(x x1)

y 6 = (x 4)

Done!Done!


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REVIEW----Every function has a formula that can be

written many different ways.

-Slope-Intercept Form: A formula where the

yis by itselfit tells us the y-intercept, andthe slope. y = mx + b

-Point-Slope Form: A formula where anypoint can be used along with the slope.

y y1 = m(x x1)


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Question: Write out the Point-Slope & Slope

Interceptformula for a function that passes

through the points (9,17) & (-4, 5).

STEP 3: Now we just

need to find theY-Interceptto

complete the SLOPE-

INTERCEPT FORM.HINT: Use the Slope

Intercept Form, and

just plug one of the

points!

y = mx + b

m =12

13 x = -4 y = 5

5= 12(-4) + b 13


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Slope-Intercept Form:

y = mx + bPoint-Slope Form:

y y1 = m(x x1)


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One More Form

The third kind of form has both theXand Yon

the same side of the equation:

x + y =

This is called STANDARD FORM.

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