1. Perpendicular and Parallel Lines

2. Parallel and Perpendicular Lines are parallel when they have the same slope Lines are perpendicular when the product of the slopes is -1 e.g. 3 and -1/3 y = 3 x + 23 y = -1/3 x - 9 These lines are perpendicular

3. Example 6-1a Write the slope-intercept form of an equation for the line that passes through (4, –2) and is parallel to the graph of The line parallel tohas the same slope, Replace m with and (x, y) with (4, -2) in the point-slope form.

4. Example 6-1b Point-slope form Replace m with y with – 2, and x with 4. Simplify. Distributive Property Subtract 2 from each side.

5. Example 6-1c Write the equation in slope- intercept form. Answer:The equation is

6. Example 6-1d CheckYou can check your result by graphing both equations. The lines appear to be parallel. The graph of passes through (4, –2).

7. Example 6-1e Write the slope-intercept form of an equation for the line that passes through (2, 3) and is parallel to the graph of Answer:

8. Example 6-2d The graph shows the diagonals of a rectangle. Determine whether is perpendicular to Answer: The slope of is and the slope of is Sinceis not perpendicular to

9. Example 6-3a Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of Step 1Find the slope of the given line. Original equation Subtract 7x from each side. Simplify.

10. Example 6-3b Divide each side by –2. Simplify.Step 2The slope of the given line isSo, the slope of the line perpendicular to this line is the opposite reciprocal ofor

11. Example 6-3c Step 3Use the point-slope form to find the equation. Point-slope form and Simplify. Distributive Property

12. Example 6-3d Subtract 1 from each side. Simplify. Answer: The equation of the line is

13. Example 6-3e CheckYou can check your result by graphing both equations on a graphing calculator. Use the CALC menu to verify that passes through (4, –1).

14. Example 6-3f Write the slope-intercept form for an equation of a line that passes through (–3, 6) and is perpendicular to the graph of Answer:

15. Example 6-4a Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6). Step 1Find the slope of Original equation Subtract 5x from each side. Simplify.

16. Example 6-4b Divide each side by 2. Simplify.Step 2The slope of the given line isSo, the slope of the line perpendicular to this line is the opposite reciprocal ofor

17. Example 6-4c Step 3Substitute the slope and the given point into the point-slope form of a linear equation. Then write the equation in slope-intercept form. Point-slope form Replace x 1 with 0, y 1 with 6, and m with Distributive Property Answer: The equation of the line is

18. Example 6-4d Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through the x -intercept of that line. Answer:

20. What are the intercepts?

21. Y-Intercept = 7 X-Intercept = -7

22. Y-Intercept = -7 X-Intercept = 5

23. Y-Intercept = -3 X-Intercept = -4

24. Y-Intercept = -4X-Intercept = 1

25. Y-Intercept = 4 No X-Intercept

26. Y-Intercept = 0 X-Intercept = 0

27. No Y-Intercept X-Intercept = -5

28. Y-Intercept = -5 X-Intercept = 4

29. X and Y Intercepts What are the coordinates of the points in each of the preceding problems?

30. Y-Intercept = 7 Point is (0,7) X-Intercept = -7 Point is (-7,0)

31. Y-Intercept = -7 Point is (0,-7) X-Intercept = 5 Point is (5,0)

32. Y-Intercept = -3 Point is (0, -3) X-Intercept = -4 (-4, 0)

33. Y-Intercept = -4 Point is (0, -4) X-Intercept = 1 Point is (1,0)

34. Y-Intercept = 4 Point is (0,4) No X-Intercept

35. Y-Intercept = 0 Point is (0,0) X-Intercept = 0 Point is (0,0)

36. No Y-Intercept X-Intercept = -5 Point is (-5,0)

37. Y-Intercept = -5 Point is (0,-5) X-Intercept = 4 Point is (4,0)

38. X and Y Intercepts The x-intercept occurs when the y-coordinate is zero The y-intercept occurs when the x-coordinate is zero

39. X and Y Intercepts The x-intercept occurs when the y-coordinate is zero The y-intercept occurs when the x-coordinate is zero You can solve an equation for the point where a value is zero to find the intercept

40. X and Y Intercepts Where does the y intercept occur? When the x value is zero

41. X and Y Intercepts What is the y-intercept of the graph of the following equation? y = 4x - 2 -2

42. X and Y Intercepts What is the x-intercept of the graph of the following equation? y = 4x - 2 1/2

43. X and Y Intercepts What is the y-intercept of the graph of the following equation? 3x + 5y – 4 = 0 4/5

44. X and Y Intercepts What is the x-intercept of the graph of the following equation? 3x + 5y – 4 = 0 4/3

46. Homework 5-6 Parallel and Perpendicular Lines Two Pages All Problems