4-4 Parallel and Perpendicular Lines Goal: Write an equation of a line that is parallel or perpendicular to a given line. Eligible Content: A1.1.2.1.1 / A1.1.2.1.3

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

Examples Decide if the lines are parallel. y = 2x + 7 and y = 5 – 2x NO m = 2 and m = -2 3x + y = 15 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

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

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

Summary

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

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

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 = − 2 3 x + 4 y = 3 2 x + 12 (7, -1), 7x – 2y = 3 y = − 2 7 x + 1

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.

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.

Practice Page 242 #1, 2, 5-8

Homework Page 243 #12-16 even #21-22 #24-28 even