2.9A Parallel and Perpendicular Lines
Warm Up
Solve each equation for y.
1. y – 6x = 9
2. 4x – 2y = 8
2.9A Parallel and Perpendicular Lines
Objectives
Graph lines and write their equations in
slope-intercept and point-slope form.
Classify lines as parallel, intersecting, or coinciding.
Pairs of Lines
Parallel Lines
Perpendicular Lines Intersecting Lines
Same slope &
Slopes are opposite Different slopes
Relationship different y-intercept reciprocals
Example
𝑦 = 𝟓𝑥 + 8
𝑦 = 𝟓𝑥 − 4
𝟑
𝑦 = 𝑥−7
𝟒
𝟒
𝑦 =− 𝑥+2
𝟑
𝑦 = 𝟑𝑥 − 6
𝑦 = 𝟐𝑥 − 9
Decide whether the lines are parallel, perpendicular, or neither.
** You will sometimes need to first: solve the equations for y, and
then: identify the slopes to answer the problem.
Example 1:
y = 3x + 7
y = –3x – 4
Example 2:
𝑥 + 3𝑦 = 5
6𝑦 = −2𝑥 + 12
Example 3:
2y – 4x = 16
y – 10 = 2(x - 1)
Example 4:
3x + 5y = 2
3x + 6 = -5y
Example 5:
2y = 4x + 12
4x – 2y = 8
State what the slope would be for a parallel line and for a
perpendicular line to the given line.
** You may need to first solve the equation for y in order to
identify the slope.
Example 6:
3x + 5y = 2
Example 7:
y – 5 = 2(x + 3)
Example 8:
3x + 6 = -5y
Example 9:
Find the slope and the y-intercept of each line to write the
equation of the line in slope-intercept form.