1. Parallel & Perpendicular Lines

2. Parallel Lines have the same Slope (or same Rise/Run)

3. Finding the Slope of a Line Parallel to another Line is a No Brainer

4. Find the slope of a line Parallel to y=3x+5 Slopes of Parallel Lines

5. Find the slope of a line Parallel to y=3x+5 Slopes of Parallel Lines 1. Solve the equation for y.

6. Find the slope of a line Parallel to y=3x+5 Slopes of Parallel Lines 1.Solve the equation for y. (Already done in this case) y=3x+5 This puts the equation in Slope intercept form so Slope is # in front of x. Ans. Is 3

7. Find the slope of a line Parallel to y=2x+9 Slopes of Parallel Lines 1.Solve the equation for y.

8. Find the slope of a line Parallel to y=2x+9 Slopes of Parallel Lines 1.Solve the equation for y. (Already done in this case) Ans. Is 2 y=2x+9

9. Find the slope of a line Parallel to 2y=8x+16 Slopes of Parallel Lines 1.Solve the equation for y.

10. Find the slope of a line Parallel to 2y=8x+16 Slopes of Parallel Lines 1.Solve the equation for y. Ans. Is 4 2y=8x+16 222 y=4x+8

11. Find the slope of a line Parallel to: 1.

12. Find the slopes of a line Parallel to: 1. ANSWER IS 9 / 5

13. Find the slopes of a line Parallel to: 2. 3. 4. 5. 6.

14. Find the slopes of a line Parallel to: 2. 3. 4. 5. 4 44

15. 6. +3 1.Solve the equation for y.

16. Given the equation of one line y= 1 / 2 x +1 (0,1)

17. Find the equation of a parallel line through a point y= 1 / 2 x +1 (2,-1)

18. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines

19. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines 1.Solve the equation for y to find slope. (Already done in this case) y=3x+5 Slope Is 3 y=3x+5

20. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines 1.Solve the equation for y to find slope. 2.Put slope & (x,y) point into y=mx+b to find b. y=3x+5 Slope Is 3 xy y=3x+5 3=3(4)+b 3=12+b -9=b -12

21. Find the eq. of a line Parallel to y=3x+5 and Through Point (4,3) Equations of Parallel Lines 1.Solve the equation for y to find slope. 2.Put slope & (x,y) point into y=mx+b to find b. 3.Put m&b (from steps 1&2) into y=mx+b To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK) y=3x+5 3=3(4)+b 3=12+b -9=b Slope Is 3 -12 xy y=3x-9 1. 2. 3.

22. Find the eq. of a line Parallel to y=-2x+6 and Through Point (5,1) Equations of Parallel Lines 1.Solve the equation for y to find slope. 2.Put slope & (x,y) point into y=mx+b to find b. 3.Put m&b (from steps 1&2) into y=mx+b

23. Find the equation of a line Parallel to given line and through Pt: 1. (4,-2) 2. (-3,-6) 3. (5,8)

24. Slopes of Perpendicular Lines NEG RECIPROCAL (Double Switch)

25. (3,2) (6,4) (0,0) 1 2 3 1 2 4 3 56 4 2 3 -3 2 Perpendicular Line

26. How to remember Perpendicular Lines have NEG-RECIPROCAL Slopes

28. Perpendicular Lines have NEG- RECIPROCAL Slopes

29. What is the NEG-RECIPROCAL 1.

30. What is the NEG-RECIPROCAL 1. -3 2

31. What is the NEG-RECIPROCAL 2.

32. What is the NEG-RECIPROCAL 2. 3 5

33. What is the NEG-RECIPROCAL 3.

34. What is the NEG-RECIPROCAL 3. 8 7

35. What is the NEG-RECIPROCAL 4.

36. What is the NEG-RECIPROCAL 4. 7

37. What is the NEG-RECIPROCAL 5. 6.

38. What is the NEG-RECIPROCAL 5. 6. 1 10 5 9

39. Solving for the equation of a line perpendicular to another line & through the point (0,-3). (0,-3) Given line y=x+3

40. Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines

41. Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines 1. Solve the equation for y.

42. Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines 1.Solve the equation for y. (Slope is Neg. Reciprocal) y=3x+5 Perpendicular slope is -1/3

43. Find the slope of a line Perpendicular to y=2x+9 Slopes of Perpendicular Lines 1.Solve the equation for y.

44. Find the slopes of a line Perpendicular to: 1. 2. 3. 4. 5. 6.

45. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines

46. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines 1.Solve the equation for y to find slope. (Slope is Neg. Reciprocal) y=3x+5 Slope Is 3 Neg Recip Is -1/3 y=3x+5

47. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines 1.Solve the equation for y to find slope. (Use Neg Recip) 2.Put slope & (x,y) point into y=mx+b to find b. y=3x+5 xy +4/3 Slope Is 3 Neg Recip Is -1/3

48. Find the eq. of a line Perpendicular to y=3x+5 and Through Point (4,3) Equations of Perpendicular Lines 1.Solve the equation for y to find slope. (Use Neg Recip) 2.Put slope & (x,y) point into y=mx+b to find b. 3.Put m&b (from steps 1&2) into y=mx+b To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK) y=3x+5 xy +4/3 Slope Is 3 Neg Recip Is -1/3

49. Find the eq. of a line Perpendicular to y=-2x+6 and Through Point (5,1) Equations of Perpendicular Lines 1.Solve the equation for y to find slope. (Use Neg Recip) 2.Put slope & (x,y) point into y=mx+b to find b. y=-2x+6 xy -5/2 Slope Is -2 Neg Recip Is 1 / 2

50. Find the eq. of a line Perpendicular to y=-2x+6 and Through Point (5,1) Equations of Perpendicular Lines

51. Find the eq. of a line Perpendicular to y=-2x+6 and Through Point (5,1) Equations of Perpendicular Lines 1.Solve the equation for y to find slope. (Use Neg Recip) y=-2x+6 Slope Is -2 Neg Recip Is 1 / 2

52. Find the eq. of a line Perpendicular to y=-2x+6 and Through Point (5,1) Equations of Perpendicular Lines 1.Solve the equation for y to find slope. (Use Neg Recip) 2.Put slope & (x,y) point into y=mx+b to find b. y=-2x+6 xy -5/2 Slope Is -2 Neg Recip Is 1 / 2

53. Find the eq. of a line Perpendicular to y=-2x+6 and Through Point (5,1) Equations of Perpendicular Lines 1.Solve the equation for y to find slope. (Use Neg Recip) 2.Put slope & (x,y) point into y=mx+b to find b. 3.Put m&b (from steps 1&2) into y=mx+b To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK) y=-2x+6 xy -5/2 Slope Is -2 Neg Recip Is 1 / 2

54. Find the equation of a line Perpendicular to given line and through Pt: 1. (4,-2) 2. (-3,-6) 3. (5,8)

55. Find the equation of a line Perpendicular to given line and through Pt: 1. (4,-2) 2. (-3,-6) 3. (5,8)

56. Review Parallel Lines Parallel lines have the same slope To find the slope of a parallel line solve equation for y To find the equation of a parallel line Solve for y to get slope (m) Put m and (x,y) point into y=mx+b to get b. Put m & b back into y=mx+b (leave x&y)

57. Review Perpendicular Lines Perpendicular lines have the negative reciprocal slope To find the slope of a perpendicular line solve equation for y To find the equation of a perpendicular line Solve for y to get slope (negative reciprocal) Put m and (x,y) point into y=mx+b to get b. Put m & b back into y=mx+b (leave x&y)

58. Parallel Lines Parallel lines have the same slope To find the slope of a parallel line solve equation for y To find the equation of a parallel line Solve for y to get slope (m) Put m and (x,y) point into y=mx+b to get b. Put m & b back into y=mx+b (leave x&y) Perpendicular Lines Perpendicular lines have the negative reciprocal slope To find the slope of a perpendicular line solve equation for y To find the equation of a perpendicular line Solve for y to get slope (negative reciprocal) Put m and (x,y) point into y=mx+b to get b. Put m & b back into y=mx+b (leave x&y)

59. Parallel Lines Perpendicular Lines