Algebra 1 Common Core Student Edition, Grade 8-9

Why start with
point-slope form?
You k no w a p o in t on the
line. You can use w ha t
you know about parallel
lines to find the slope.
So, point-slope form is
convenient to use.

Pr o b l em 1 Writing an Equation of a Parallel Line

A line passes through (12, 5) and is parallel to the graph of y = |x — 1. What

equation represents the line in slope-intercept form?

Step 1 Identify th e slope of th e given line. The slope of th e graph of y = | x - 1 is §.

The parallel line has th e sam e slope.

Step 2 W rite an eq u a tio n in slope-intercept form of th e line th rough ( 12 , 5 ) w ith

slope |.

y - jq = m [x - xx) Start w ith point-slope form.

y- 5 = g(x- 12) S u b stitu te (12, 5) fo r (xx, y x) and |form.

y - 5 = gX -^2 23 (12) Distributive Property

y - 5 = 3 X - 8

y = | x — 3

Simplify.

A dd 5 to each side.

The g raph of y = 3 X - 3 passes th rough (12, 5) an d is parallel to th e g raph of

y = f x - L

G o t It? 1. A line passes th rough ( - 3 , - 1 ) a n d is parallel to th e g raph of y = 2x + 3.

W hat eq u a tio n rep resen ts th e line in slope-intercept form?

You can also use slope to d eterm in e w h e th e r two lines are perpendicular.

Perpendicular lines are lines th a t in tersect to form right angles.

Key Concept Slopes o f P erpendicular Lines

Words Graph

Two nonvertical lines are p erp en d icu lar if th e p ro d u ct

of their slopes is - 1. A vertical line an d a horizontal

line are also perpendicular.

Example

The g raph of y = \x - 1 has a slope of

The g raph of y = —2x + 1 has a slope of —2.

Since | ( —2) = — 1, th e lines are p erpendicular.

V _____ , J

Two n u m b ers w hose p ro d u c t is - 1 are opposite reciprocals. So, th e slopes of

p erp en d icu lar lines are opposite reciprocals. To find th e opposite reciprocal

of - 1, for example, first find th e reciprocal, - |. Then w rite its opposite, |.

Since — |* |= —1, |is th e opposite reciprocal of - |.