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# Slope (Algebra 2)

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Students learn the definition of slope and calculate the slope of lines.
Students also learn to consider the slopes of parallel lines and perpendicular lines.

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### Slope (Algebra 2)

1. 1. Slope
2. 2. Vocabulary <ul><li>Find and use the slope of a line. </li></ul><ul><li>Graph parallel and perpendicular lines. </li></ul>1) slope 2) rate of change Slope
3. 3. If the pilot doesn’t change something, he / she will not make it home for Christmas. Would you agree?
4. 4. Consider the options: 1) Keep the same slope of his / her path.
5. 5. Consider the options: 1) Keep the same slope of his / her path.
6. 6. Consider the options: 1) Keep the same slope of his / her path. Not a good choice!
7. 7. Consider the options: 1) Keep the same slope of his / her path. Not a good choice! 2) Go straight up.
8. 8. Consider the options: 1) Keep the same slope of his / her path. Not a good choice! 2) Go straight up.
9. 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. 10. Fortunately, there is a way to measure a proper “ slope ” to clear the obstacle.
11. 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. 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. 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. 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. 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. 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. 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. 18. y x 10000 10000 0 0
19. 19. FINDING THE SLOPE OF A LINE Slope x y
20. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 31. Slope Find the slope of the line. y x (2, 3) (8, 8)
32. 32. Slope Find the slope of the line. y x (2, 3) (8, 8)
33. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 43. Graph the line passing through point (1, 1) with a slope of 2. Slope y x
44. 44. Graph the line passing through point (1, 1) with a slope of 2. 1) Graph the point (1, 1). Slope y x
45. 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. 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. 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. 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. 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. 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. 51. y x If the line rises to the right, then the slope is positive. Slope
52. 52. y x If the line rises to the right, then the slope is positive. Slope
53. 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. 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. 55. Slope y x If the line is horizontal, then the slope is zero.
56. 56. Slope y x If the line is horizontal, then the slope is zero.
57. 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. 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. 59. Slope In a plane, nonvertical lines _________________ are parallel . y x
60. 60. Slope In a plane, nonvertical lines _________________ are parallel . with the same slope y x
61. 61. Slope In a plane, nonvertical lines _________________ are parallel . with the same slope y x
62. 62. Slope In a plane, nonvertical lines _________________ are parallel . with the same slope y x
63. 63. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. Slope y x
64. 64. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. negative reciprocal Slope y x
65. 65. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. negative reciprocal Slope y x
66. 66. In a plane, nonvertical lines are perpendicular if and only if their slopes are _________________. negative reciprocal Slope y x
67. 67. Slope End of Lesson
68. 68. Credits PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant http://robertfant.com