This document discusses parallel and perpendicular lines. It defines parallel lines as having the same slope and perpendicular lines as having slopes that are negative reciprocals of each other. It provides examples of finding equations of lines parallel or perpendicular to given lines using their slopes. It also covers finding the slope of a line perpendicular to a given line, writing equations in point-slope and slope-intercept form for lines perpendicular to other lines, and identifying slopes from equations written in various forms.

1. 5.6 Parallel & Perpendicular Lines

2. 1. Parallel lines have the same slope Slope of Line A = Slope of Line B = Slope of Line A = Line A Line B 1 1 Slope of Line B

3. 2. Perpendicular lines slope at 90° Slope of Line A = Slope of Line B = Slope of Line A = Line A Line B 1 -1 Opposite Reciprocal of Line B

4. Write an equation in slope-intercept form for the line parallel to each line below with a y-intercept of 3 . Y = 4x + 2 Step 1: Identify Slope M = _________ Step 2: Write equation Y = mx + b Y = ___x + _____

5. Write an equation in slope-intercept form for the line parallel to each line below with a y-intercept of 3. 4. Y = -3x - 2 Step 1: Identify Slope M = _________ Step 2: Write equation Y = mx + b Y = ___x + _____

6. 6. Find a perpendicular slope of the following slopes. 6. Slope = 1/2 Perpendicular Slope = _______

7. 7. Find a perpendicular slope of the following slopes. 7. Slope = 5/6 Perpendicular Slope = _______

8. 8. Find a perpendicular slope of the following slopes. 8. Slope = -4 Perpendicular Slope = _______

9. Find the slope of a line that is perpendicular to the following lines. 9. Y = 3x + 2 Slope = _______ Perpendicular Slope = __________

10. Find the slope of a line that is perpendicular to the following lines. 10. 3x + 12y = 12 Slope = _______ Perpendicular Slope = __________

11. Write an equation in point-slope form for the line that contains the point (-3, 4), and is perpendicular to the graph of the equation. Y = 2x + 3 Step 1: Identify Slope Slope = _______ Perpendicular Slope = ______ Step 2: Write Equation y – y 1 = m (x – x 1 ) y - ___ = ___(x -____) __________________________

12. Write an equation in point-slope form for the line that contains the point (-3, 4), and is perpendicular to the graph of the equation. 3x + y = 7 Step 1: Identify Slope Slope = _______ Perpendicular Slope = ______ Step 2: Write Equation y – y 1 = m (x – x 1 ) _________________________ __________________________

13. Write an equation in slope-intercept form that is perpendicular to the given line. 15. (-3, -5), y = 3x - 1 Step 1: Identify Slope Slope (m) = _______ Perpendicular Slope = __ Step 2: Write Equation Y = mx + b _____ = _____(____) + b b = _______________

14. 15. Write an equation in slope-intercept form that is perpendicular to the given line. M = -1/3 b = -6 Y = mx + b Y = ____x + ______

15. Write an equation in slope-intercept form that is perpendicualr to the given line. 16. (5, 4) y - 10 = -5 x 2 Step 1: Identify Slope Slope (m) = _______ Perpendicular Slope = __ Step 2: Write Equation Y = mx + b _____ = _____(____) + b b = _______________

16. 16. Write an equation in slope-intercept form that is perpendicular to the given line. M = 2/5 b = 2 Y = mx + b Y = ____x + ______