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

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