Algebra 1 Common Core Student Edition, Grade 8-9

Think....
Why write each
equation in slope-
in te rc e p t fo rm?
You can easily identify
the slope of an equation
in slope-intercept
form. Just look at the
coefficient of x.

Classifying Lines

Are the graphs of 4y = -5x+ 12 and y = |x - 8 parallel, perpendicular, or

neither? Explain.

Step 1 Find th e slope of each line by w riting its eq u a tio n in slope-intercept form, if

necessary. Only th e first equ atio n n ee d s to be rew ritten.

4 y = —5x + 12 Write the first equation.

Y = 5 x 4+ 12 D ivide each side by 4.

y = - ^x-t- 3 Simplify.

The slope of the graph of y = -\x 4- 3 is —§.

The slope of th e graph of y = | x - 8 is |.

Step 2 The slopes are n o t th e sam e, so th e lines ca n n o t b e parallel. M ultiply th e

slopes to see if they are opposite reciprocals.

-5.4= -!

4 5 1

The slopes are opposite reciprocals, so th e lines are perpendicular.

s j G o t It? 2. Are th e graphs of th e equations parallel, perpendicular, or neitherl Explain.

a. y = 4x 4-7 and 4x - 3y = 9 b. 6 y = - x 4- 6 an d y : ~X 4- 6

Think
How do you know
you have found the
opposite reciprocal?
Multiply the two
numbers together as a
check. If the product is

• 1 , the numbers are
  opposite reciprocals:
  |(—3) = -1.

Problem 3 Writing an Equation of a Perpendicular Line

Multiple Choice Which equation represents the line that passes through (2 ,4 ) and

is perpendicular to the graph of y = |x — 1?

Ca") y = qX + (^10) CjD y = 3x 4-10 C O y = - 3 x - 2 y = — 3x 4- 10
Step 1 Identify th e slope of th e graph of th e given equation. The slope is 3.
S te p 2 Find th e opposite reciprocal of th e slope from Step 1. The opposite reciprocal
of | is —3. So, th e p erp en d icu lar line h as a slope of —3.
Step 3 Use point-slope form to write an eq u a tio n of th e p erp en d icu lar line.
y — yj = m (x - x t ) Write point-slope form,
y - 4 = - 3 ( x - 2) Substitute (2,4) for (x1f y{) and - 3 fo r m.
y - 4 = — 3x 4- 6 Distributive Property
y = - 3 x 4- 10 A dd 4 to each side.
The equ atio n is y = — 3x 4-10. The correct answ er is D.
& G o t It? 3. A line passes through ( 1 , 8 ) an d is p erp en d icu lar to th e graph of
y = 2 x 4- 1. W hat eq u a tio n represents th e line in slope-intercept form?
332 C h a p te r 5 Linear Funct ions