1. 3.3 – Slope

2. Recall how to graph y = 2x – 3. 3.3 – Slope

3. Recall how to graph y = 2x – 3. 3.3 – Slope

4. Recall how to graph y = 2x – 3. x 3.3 – Slope

5. Recall how to graph y = 2x – 3. x 0 1 3.3 – Slope

6. Recall how to graph y = 2x – 3. x2x – 3 0 1 3.3 – Slope

7. Recall how to graph y = 2x – 3. x2x – 3y 0 1 3.3 – Slope

8. Recall how to graph y = 2x – 3. x2x – 3y(x, y) 0 1 3.3 – Slope

9. Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

10. Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

11. Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

12. Recall how to graph y = 2x – 3. x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1) 3.3 – Slope

13. Slope

14. Slope = Change in y Change in x

15. Slope = Change in y Change in x m = y 2 – y 1 x 2 – x 1

16. Slope = Change in y Change in x m = y 2 – y 1, x 2 – x 1 for (x 1,y 1 ) and (x 2,y 2 )

17. Slope = Change in y Change in x m = y 2 – y 1, x 2 – x 1 for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

18. Slope = Change in y Change in x m = y 2 – y 1, Slope = x 2 – x 1 for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

19. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

20. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

21. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

22. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

23. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

24. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

25. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256*

26. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4)

27. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4)

28. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) m = y 2 – y 1 x 2 – x 1

29. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 m = y 2 – y 1 x 2 – x 1

30. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 m = y 2 – y 1 x 2 – x 1

31. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 m = y 2 – y 1 x 2 – x 1

32. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1

33. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) (3 – (-1))

34. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

35. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

36. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

37. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

38. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2

39. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 1

40. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 1

41. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 2 1

42. Slope = Change in y Change in x m = y 2 – y 1, Slope = rise x 2 – x 1 run for (x 1,y 1 ) and (x 2,y 2 ) *See bottom p.256* Ex. 1 Find the slope of the lines through the following points: a. (-1,2) and (3,4) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1 = (4 – 2) = 1 (3 – (-1)) 2 2 1

43. b.

44. b. Slope =

46. b. Slope = -1

48. 3

49. b. Slope = -1 3 c. (1,2) and (-1,2)

50. b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2

51. b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 x 2 – x 1

52. b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 = (2 – 2) x 2 – x 1 -1 – 1

53. b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 = (2 – 2) = 0 x 2 – x 1 -1 – 1 -2

54. b. Slope = -1 3 c. (1,2) and (-1,2) x 1 y 1 x 2 y 2 m = y 2 – y 1 = (2 – 2) = 0 = 0 x 2 – x 1 -1 – 1 -2

55. Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in 1998. Based on this information, at what rate did the average annual household income change per year.

58. ***Time is always the independent (x) variable!

59. Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in 1998. Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 x 2 – x 1

60. Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in 1998. Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 x 2 – x 1

61. Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in 1998. Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990)

62. Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in 1998. Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990) = 7144 8

63. Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in 1998. Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990) = 7144 8 = 893

64. Ex. 2 In 1990, the average annual household income was $55,280. It then rose to $62,424 in 1998. Based on this information, at what rate did the average annual household income change per year. ***Time is always the independent (x) variable! m = y 2 – y 1 = (62,424 – 55,280) x 2 – x 1 (1998 – 1990) = 7144 8 = 893 = $893/yr.