Algebra 1 Common Core Student Edition, Grade 8-9

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Since you know a point
and the slope, use
point-slope form.

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How does the

equation help you

make a graph?

Use the point from the

equation. Use the slope

from the equation to find

another point. Graph

using the tw o points.

Here's W hy It W orks Given a p o in t {xv y j on a line an d the line's slope m, you

can use the definition of slope to derive point-slope form.

Vo — Vi

Xz x~ - = m Use th e d e fin itio n o f slope.

y — y,

= m Let (x, y) be any p oin t on the line. Substitute (x, y) for (x2, y2).

x — x

y-y i

X

(x - x 2) = m(x - x2) Multiply each side by (x - x-|).

y - yx = m{x - x 2) Simplify the left side of the equation.

Problem 1 Writing an Equation in Point-Slope Form

A line passes through ( - 3 ,6 ) and has slope - 5. What is an equation of the line?

y - yl = m (x - xx) Use p oin t-slo pe form.

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y — 6 = —5 [ x - ( ~ 3 ) ] S ub stitu te ( - 3 , 6) fo r (x1( y{) and - 5 for m.

y — 6 = -5(x + 3) Simplify inside grouping symbols.

G o t It? 1. A line passes th rough (8, - 4 ) an d h as slope |. W hat is an e q u a tio n in

point-slope form of the line?

Problem 2 Graphing Using Point-Slope Form

W hat is th e g ra p h of th e e q u a tio n y - 1 = j ( x - 2)?

The equ atio n is in point-slope form, y — y \ = m{x - x{). A p o in t (x1; y x) on th e line is

(2,1), an d th e slope m is |.

Step 1

Go t I t? 2. W hat is the graph of th e eq u a tio n y + 7 = —l ( x - 4)?

Step 3 Draw a line through!

the tw o points.

G ra p h a p o in t

at (2,1).

Step 2 Use th e slope, Go

up 2 u n its a n d r ig h t

3 u n its. D ra w a p o in t.

316 Chapters Lin ear Fu n ct io n s