1. 4-4 Parallel and Perpendicular Lines
Goal:
Write an equation of a line that is parallel or perpendicular to a given line.
Eligible Content:
A / A

2. Summary

3. Vocabulary Parallel Lines Not Parallel Lines
Parallel Lines - two lines that have the same slope.
y = 2x + 4
y = 2x – 8
y = -3x + 7
y = 3x – 3
Parallel Lines
Not Parallel Lines

4. Examples Decide if the lines are parallel. y = 2x + 7 and y = 5 – 2x
NO m = 2 and m = -2
3x + y = and y = -3x + 7
YES m = -3 and m = -3
6x + 9y = 18 and 4x + 6y = 30
YES m = -2/3 and m = -2/3

5. Vocabulary Perpendicular Lines Not Perpendicular Lines
Perpendicular Lines - two lines whose slopes are opposite reciprocals.
y = 3x + 4
y = − 1 3 x + 7
y = 2x + 7
y = -2x - 3
Perpendicular Lines
Not Perpendicular Lines

6. Examples Decide if the lines are perpendicular.
y = 2x and y = 5 – 2x
NO m = 2 and m = -2
y = 1 3 x and y = -3x + 7
YES m = and m = -3
2x + 5y = 20 and 6x + 15y = 90
NO m = − and m = − 2 5

7. Determine whether the graphs of
y = –2x + 1 and x – 2y = –4 are parallel or perpendicular.
A. perpendicular
B. parallel
C. Neither

8. Writing Equations
Write the equation of the line that goes through each point and is parallel to the given line.
(-3, 5), y = 2x – 4
y = 2x + 11
(4, -2), y = 1 2 x – 7
y = 1 2 x – 4
(6, 3), 5x + y = 12
y = -5x + 33

9. Writing Equations
Write the equation of the line that goes through each point and is perpendicular to the given line.
(4, 7), y = 2 3 x – 1
y = − 3 2 x + 13
(-4, 6), y = −2x + 4
y = 1 2 x + 8
(7, -1), 7x – 2y = 3
y = − 2 7 x + 1

10. Write the slope-intercept form of an equation for the line that passes through (2, 3) and is parallel to the graph of y = 𝟏 𝟐 x- 1. A. B. C. D.

11. Write an equation in slope-intercept form for the line that passes through (–3, –2) and is perpendicular to the graph of x + 4y = 12. A. B. C. D.

12. Practice
Page 242 #1, 2, 7, 8

13. Homework
Page 243 #12, 14, 26, 28
#33-38