Algebra 1 Common Core Student Edition, Grade 8-9

Standard Form

@ Common Core State Standards

A-CED.A.2 Cr ea t e eq u at i o n s i n t w o o r m o r e v a r i a b l e s.

graph equations on coordinate ax es... A lso F-IF.B.4,

F-IF.C.7a, F-LE.A.2, F-LE.B.5

MP 1, M P 2, M P3. M P 4

Objectives To graph linear eq u atio n s using intercepts

To write linear eq u atio n s in stan d ard form

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f ' Getting Ready!

A point on th e graph

te lls you (ounces

of cashews,ounces

of peanuts). What

do you do w ith th is

in fo rm a tio n to fin d

th e grams o f protein?

An at h l et e w an t s t o m ake a sn ack m ix o f p ean u t s

and cash ew s t h a t will co n t ai n a cer t ai n am ount o f

protein. Cashews have 4 g of protein per ounce,

and p ean u t s have 7 g o f p r o t ein p er ounce.

How many gram s of prot ein will t h e at h let e' s mix

cont ain? W h at do t h e point s (7, 0) and (0, 4)

represent? Explain.

Snack M ix

3 0 — — — — —

° 0 1 2 3 4 5 6 7

Ounces o f cashews

mathematical In this lesson, you will learn to use intercepts to graph a line. Recall th a t a y-intercept

PRACTICES

Lesson
Vocabulary
x-intercept
standard form of
a lin e a r e q u a tio n

is th e y-coordinate of a p o in t w here a g raph crosses th e y-axis. The x-intercept is the

x-coordinate of a p o in t w here a graph crosses th e x-axis.

Esse n t i a l U n d e r st a n d i n g O ne form of a lin ear equation, called standard form,

allows you to find intercepts quickly. You can use the intercepts to draw the graph.

Key Concept Standard Form of a Linear Equation

The standard form of a linear equation is A x + By = C, w here A, B, an d C are real

numbers, and A and B are n o t b o th zero.

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Why do you

substitute 0 fo r y to

fin d th e x -in te rc e p t?

The x-intercept is the

x-coordinate o f a point

on the x-axis. Any point

on the x-axis has a

y-coordinate o f 0.

Finding x - and y-lntercepts

W hat a re th e x- and y-in te rc e p ts of th e g ra p h o f 3x + 4y = 24?

Step 1 To find th e x-intercept,

substitute 0 fory. Solve forx.

3x + 4y = 24

3x + 4(0) = 24

3x = 24

x = 8

The x-intercept is 8.

Step 2 To fin d t h e y -in te rc e p t,

substitute 0 forx. Solve fory.

3x + 4y = 24

3(0) + 4y = 24

4y — 24

y = 6

The y -intercept is 6.

Chap t er 5 Linear Funct ions

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