The document explains the concept of slope in relation to lines on a graph, emphasizing methods for calculating and interpreting slope in real-world scenarios, such as flight paths. It distinguishes between various types of slopes, including positive, negative, zero, and undefined, and describes conditions for parallel and perpendicular lines based on their slopes. Visual examples are included to illustrate how to graph lines and calculate their slopes using given points.

1. Slope

2. Vocabulary Find and use the slope of a line. Graph parallel and perpendicular lines. 1) slope 2) rate of change Slope

3. If the pilot doesn’t change something, he / she will not make it home for Christmas. Would you agree?

4. Consider the options: 1) Keep the same slope of his / her path.

5. Consider the options: 1) Keep the same slope of his / her path.

6. Consider the options: 1) Keep the same slope of his / her path. Not a good choice!

7. Consider the options: 1) Keep the same slope of his / her path. Not a good choice! 2) Go straight up.

8. Consider the options: 1) Keep the same slope of his / her path. Not a good choice! 2) Go straight up.

9. Consider the options: 1) Keep the same slope of his / her path. Not a good choice! 2) Go straight up. Not possible! This is an airplane, not a helicopter.

10. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle.

11. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle. We measure the “ change in height ” required and divide that by the “ horizontal change ” required.

12. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle. We measure the “ change in height ” required and divide that by the “ horizontal change ” required.

13. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle. We measure the “ change in height ” required and divide that by the “ horizontal change ” required.

14. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle. We measure the “ change in height ” required and divide that by the “ horizontal change ” required.

15. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle. We measure the “ change in height ” required and divide that by the “ horizontal change ” required.

16. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle. We measure the “ change in height ” required and divide that by the “ horizontal change ” required.

17. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle. We measure the “ change in height ” required and divide that by the “ horizontal change ” required.

18. y x 10000 10000 0 0

19. FINDING THE SLOPE OF A LINE Slope x y

20. FINDING THE SLOPE OF A LINE Slope x y The slope m of the non-vertical line passing through the points and is

21. FINDING THE SLOPE OF A LINE Slope x y The slope m of the non-vertical line passing through the points and is

22. FINDING THE SLOPE OF A LINE Slope x y The slope m of the non-vertical line passing through the points and is

23. FINDING THE SLOPE OF A LINE Slope x y The slope m of the non-vertical line passing through the points and is

24. FINDING THE SLOPE OF A LINE Slope x y The slope m of the non-vertical line passing through the points and is

25. The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. Slope y x (1, 1) (3, 6)

26. The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. Slope y x (1, 1) (3, 6)

27. The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. Slope y x (1, 1) (3, 6)

28. The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. rise = 6 - 1 = 5 units Slope y x (1, 1) (3, 6)

29. The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. run = 3 - 1 = 2 units rise = 6 - 1 = 5 units Slope y x (1, 1) (3, 6)

30. The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. run = 3 - 1 = 2 units rise = 6 - 1 = 5 units Slope y x (1, 1) (3, 6)

31. Slope Find the slope of the line. y x (2, 3) (8, 8)

32. Slope Find the slope of the line. y x (2, 3) (8, 8)

33. Slope Find the slope of the line. run = 8 - 2 = 6 units rise = 8 - 3 = 5 units y x (2, 3) (8, 8)

34. Slope Find the slope of the line. run = 8 - 2 = 6 units rise = 8 - 3 = 5 units y x (2, 3) (8, 8)

35. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Slope y x 10 0 -5 -5 5 -5 10 -5 0 5

36. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Slope y x 10 0 -5 -5 5 -5 10 -5 0 5

37. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Slope y x 10 0 -5 -5 5 -5 10 -5 0 5

38. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Slope y x 10 0 -5 -5 5 -5 10 -5 0 5

39. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Slope y x 10 0 -5 -5 5 -5 10 -5 0 5

40. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Slope y x 10 0 -5 -5 5 -5 10 -5 0 5 -8 8

41. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Slope y x 10 0 -5 -5 5 -5 10 -5 0 5 -8 8

42. Plot the points (-4, 7) and (4, -1) and draw a line through them. Find the slope of the line passing through the points. Negative slope: Falls from left to right Slope y x 10 0 -5 -5 5 -5 10 -5 0 5 -8 8

43. Graph the line passing through point (1, 1) with a slope of 2. Slope y x

44. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). Slope y x

45. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). Slope y x 2) Follow the slope of to locate another point on the line.

46. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). Slope y x 2) Follow the slope of to locate another point on the line.

47. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). Slope y x 2) Follow the slope of to locate another point on the line.

48. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). Slope y x 2) Follow the slope of to locate another point on the line.

49. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). 3) Draw the line, connecting the two points. Slope y x 2) Follow the slope of to locate another point on the line.

50. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). 3) Draw the line, connecting the two points. Slope y x 2) Follow the slope of to locate another point on the line.

51. y x If the line rises to the right, then the slope is positive. Slope

52. y x If the line rises to the right, then the slope is positive. Slope

53. y x If the line rises to the right, then the slope is positive. Slope y x If the line falls to the right, then the slope is negative.

54. y x If the line rises to the right, then the slope is positive. Slope y x If the line falls to the right, then the slope is negative.

55. Slope y x If the line is horizontal, then the slope is zero.

56. Slope y x If the line is horizontal, then the slope is zero.

57. Slope y x If the line is horizontal, then the slope is zero. y x If the line is vertical, then the slope is undefined.

58. Slope y x If the line is horizontal, then the slope is zero. y x If the line is vertical, then the slope is undefined.

59. Slope In a plane, nonvertical lines _________________ are parallel . y x

60. Slope In a plane, nonvertical lines _________________ are parallel . with the same slope y x

61. Slope In a plane, nonvertical lines _________________ are parallel . with the same slope y x

62. Slope In a plane, nonvertical lines _________________ are parallel . with the same slope y x

63. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. Slope y x

64. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. negative reciprocal Slope y x

65. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. negative reciprocal Slope y x

66. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. negative reciprocal Slope y x

67. Slope End of Lesson

68. Credits PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant http://robertfant.com