Algebra 1 Common Core Student Edition, Grade 8-9

Slope-lntercept Form

Co m m o n Co r e St a t e St a n d a r d s

F-IF.C.7a Gr ap h l i n ear an d q u ad r at i c f u n ct i o n s

and show int ercept s, maxima, and minima. Also

A -S S E .A .1a , A -C E D .A .2 , F-IF.B.4, F-LE.A.2

MP 1, MP 2, MP 3, MP 4

Objectives To w rite linear equations using slope-intercept form

To graph linear eq u atio n s in slope-intercept form

Getting Ready! «<► X C 4

Each point o f th e

graph gives you

in fo rm a tio n about

th e bamboo plant.

Bam b oo can g r ow v er y q u i ck l y. Th e g r ap h m o d el s t h e

growth of a bamboo plant. Find the point where the

line cro sses t he vert ical axis. W hat does t his point

t el l you ab o u t t h e bamboo p l an t? Fin d t h e slo p e o f

the line. What does the slope tell you about the

bamboo plant? How do you know?

Bamboo Growth

20

l 1 0 2 0

Time (days)

MATHEMATICAL

PRACTICES

Lesson

Vocabulary

parent function

lin e a r p a re n t

fu n ctio n

lin e a r e q u a tio n

y-intercept

slope-intercept

fo rm

The function in the Solve It is a linear function, b u t it is n o t a direct variation. Direct

variations are only p a rt of th e family of lin ear functions.

A family of functions is a group of functions w ith com m on

characteristics. A parent function is th e sim plest function w ith these

characteristics. The linear parent function is y = x or / ( x ) = x. The

graphs of th ree linear functions are show n at th e right.

A linear equation is an equation th a t m odels a linear function. In a

linear equation, th e variables ca n n o t be raised to a pow er o th er th a n 1.

So y = 2x is a linear equation, b u t y = x 2 a n d y = 2* are not. The

graph of a linear equation contains all th e o rdered pairs th at are

solutions of the equation.

G raphs of linear functions m ay cross th e y-axis at any point. A

y-intercept of a graph is th e y-coordinate of a p o in t w here the

graph crosses th e y-axis.

Esse n t i a l U n d e r st a n d i n g You can use th e slope and

y-intercept of a line to w rite a n d graph an eq u a tio n of the line.

Key Concept Slope-lntercept Form of a Linear Equation

The slope-intercept form of a linear equ atio n of a nonvertical line is y = m x + b.

T T

slope y-intercept

308 Ch ap t er 5 Lin ear Fu n ct io n s