1. 4.4 – Parallel & Perpendicular Lines

2. Parallel Lines

3. Parallel Lines – slopes are the same

4. Parallel Lines – slopes are the same (m)

5. Perpendicular Lines

6. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical

7. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical

8. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -m

9. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -m

10. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m

11. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel?

12. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = ½x + 2 y = ½x – 9

13. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = ½x + 2 || y = ½x – 9

14. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = ½x + 2 || b) y = 3x – 5 y = ½x – 9 y = -⅓x + 7

15. Parallel Lines – slopes are the same (m) Perpendicular Lines – slopes are the opposite reciprical -1 m Ex. 1 Perpendicular or Parallel? a) y = ½x + 2 || b) y = 3x – 5 _|_ y = ½x – 9 y = -⅓x + 7

16. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12.

17. 1)Find the slope needed.

18. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed.

19. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed. x + 4y = 12

20. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed. x + 4y = 12 -x-x

21. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12

22. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4

23. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3

24. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼

25. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1)Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4

26. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation.

27. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation.

28. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation.

29. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 )

30. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y –

31. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y –

32. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y –

33. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) =

34. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) =

35. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) =

36. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x -

37. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x -

38. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x -

39. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3))

40. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3)

41. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12

42. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12

43. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12 - 2 - 2

44. Ex. 2 Write the slope-intercept form of the equation through (-3, -2) perpendicular to the graph of x + 4y = 12. 1) Find the slope needed. x + 4y = 12 -x-x 4y = -x + 12 4 4 4 y = -¼x + 3 m = -¼, m ┴ = 4 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (-2) = 4(x – (-3)) y + 2 = 4(x + 3) y + 2 = 4x + 12 - 2 - 2 y = 4x + 10

45. Ex. 3 Write the slope-intercept form of the equation through (9, 0) parallel to the graph of y = - ⅓ x + 2.

46. 1) Find the slope needed. y = -⅓x + 2 m = -⅓, m || = -⅓

47. Ex. 3 Write the slope-intercept form of the equation through (9, 0) parallel to the graph of y = -⅓x + 2. 1) Find the slope needed. y = -⅓x + 2 m = -⅓, m || = -⅓ 2) Use coordinate point & slope to write equation. y – y 1 = m(x – x 1 ) y – (0) = -⅓ (x – (9)) y = -⅓ (x – 9) y = -⅓ x + 3