Algebra 1 Common Core Student Edition, Grade 8-9

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Objectives To d eterm in e w h e th e r lines are parallel, perpendicular, or n eith er

To write equations of parallel lines a n d p erp en d icu lar lines

Getting Ready!

Shift your

perspective to

inclu de th e area

outside the grid

as well.

MATHEMATICAL

PRACTICES

Copy th e graph shown a t th e rig h t. Can you

draw a line t h a t will not in te rs e c t e ith e r of

th e lines in th e graph? I f so, draw th e line

I f not, why not?

Can you draw a line t h a t will in te rs e c t

one of th e lines in such a way t h a t th e

intersection forms four congruent angles?

I f so, draw th e line. I f not, why not?

4 A y

0 X

(^1) L
& L e ss o n
Vocabulary
parallel lines
perpendicular
lin e s
opposite
re cip ro c als
^ Two distinct lines in a coordinate p lan e either in tersect or are parallel. Parallel lines are
lines in th e sam e p lan e th a t never intersect.
Essent ial Und er st and ing You can d eterm in e th e relationship b etw een two lines
by comparing their slopes and y-intercepts.
Key Concept Slopes o f P arallel Lines
Words
Nonvertical lines are parallel if they have th e sam e
slope a n d different y-intercepts. Vertical lines are
parallel if they have different x-intercepts.
Graph
Parallel and
P erp en d icu la r Lines
@ C om m on C ore State Standards
G -GPE.B.5 Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
problems.
MP 1, MP 2, MP 3, MP 4, MP 7
Example
The graphs of y = gx + 1 a n d y = \ x - 2 are lines
th a t have th e sam e slope, g, an d different y-intercepts.
The lines are parallel.
You can use th e fact th a t th e slopes of parallel lines are th e sam e to write th e equation
of a line parallel to a given line.
330 C h a p te r 5 Lin ear Fu n ct io n s