Integrated Math 2 Section 6-2

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Slope of a Line

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Integrated Math 2 Section 6-2

  1. 1. Section 6-2 Slope of a Line Thursday, November 12, 2009
  2. 2. Essential Questions How do you find the slope of a line? How do you identify horizontal and vertical lines? Where you’ll see it: Business, science, transportation Thursday, November 12, 2009
  3. 3. Vocabulary 1. Slope: Thursday, November 12, 2009
  4. 4. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Thursday, November 12, 2009
  5. 5. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again. Thursday, November 12, 2009
  6. 6. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again. 1. Slope: Thursday, November 12, 2009
  7. 7. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again. 1. Slope: How steep a line is, measured in “rise over run” Thursday, November 12, 2009
  8. 8. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again. 1. Slope: How steep a line is, measured in “rise over run” Formula: Thursday, November 12, 2009
  9. 9. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again. 1. Slope: How steep a line is, measured in “rise over run” Formula: y 2 − y1 m= , for points ( x 1 , y 1 ) and ( x 2 , y 2 ) x 2 − x1 Thursday, November 12, 2009
  10. 10. MATH CALISTHENICS! Thursday, November 12, 2009
  11. 11. Example 1 Graph the line the goes through the given points, then find the slope of the line. C = (−4,0) D = (4, 4) Thursday, November 12, 2009
  12. 12. Example 1 Graph the line the goes through the given points, then find the slope of the line. C = (−4,0) C D = (4, 4) Thursday, November 12, 2009
  13. 13. Example 1 Graph the line the goes through the given points, then find the slope of the line. D C = (−4,0) C D = (4, 4) Thursday, November 12, 2009
  14. 14. Example 1 Graph the line the goes through the given points, then find the slope of the line. D C = (−4,0) C D = (4, 4) Thursday, November 12, 2009
  15. 15. Example 1 Graph the line the goes through the given points, then find the slope of the line. y 2 − y1 D m= x 2 − x1 C = (−4,0) C D = (4, 4) Thursday, November 12, 2009
  16. 16. Example 1 Graph the line the goes through the given points, then find the slope of the line. y 2 − y1 D m= x 2 − x1 C = (−4,0) C 4−0 = D = (4, 4) 4 − (−4) Thursday, November 12, 2009
  17. 17. Example 1 Graph the line the goes through the given points, then find the slope of the line. y 2 − y1 D m= x 2 − x1 C = (−4,0) C 4−0 = D = (4, 4) 4 − (−4) 4 = 8 Thursday, November 12, 2009
  18. 18. Example 1 Graph the line the goes through the given points, then find the slope of the line. y 2 − y1 D m= x 2 − x1 C = (−4,0) C 4−0 = D = (4, 4) 4 − (−4) 4 1 = = 8 2 Thursday, November 12, 2009
  19. 19. Example 1 Graph the line the goes through the given points, then find the slope of the line. y 2 − y1 D m= x 2 − x1 C = (−4,0) C 4−0 = D = (4, 4) 4 − (−4) 4 1 = = 8 2 Here, the slope tells us “Up 1, Right 2” Thursday, November 12, 2009
  20. 20. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) Thursday, November 12, 2009
  21. 21. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 Thursday, November 12, 2009
  22. 22. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3−9 Thursday, November 12, 2009
  23. 23. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3−9 0 = −6 Thursday, November 12, 2009
  24. 24. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3−9 0 = =0 −6 Thursday, November 12, 2009
  25. 25. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 m= x 2 − x1 −2 − (−2) = 3−9 0 = =0 −6 Horizontal Thursday, November 12, 2009
  26. 26. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) = 3−9 0 = =0 −6 Horizontal Thursday, November 12, 2009
  27. 27. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 12 = = 3−9 3−3 0 = =0 −6 Horizontal Thursday, November 12, 2009
  28. 28. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 12 = = 3−9 3−3 0 −16 = =0 = −6 0 Horizontal Thursday, November 12, 2009
  29. 29. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 12 = = 3−9 3−3 0 −16 = =0 = Undefined −6 0 Horizontal Thursday, November 12, 2009
  30. 30. Example 2 Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4) y 2 − y1 y 2 − y1 m= m= x 2 − x1 x 2 − x1 −2 − (−2) −4 − 12 = = 3−9 3−3 0 −16 = =0 = Undefined −6 0 Horizontal Vertical Thursday, November 12, 2009
  31. 31. Horizontal vs. Vertical Thursday, November 12, 2009
  32. 32. Horizontal vs. Vertical Horizontal lines have slopes of Thursday, November 12, 2009
  33. 33. Horizontal vs. Vertical Horizontal lines have slopes of zero Thursday, November 12, 2009
  34. 34. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Thursday, November 12, 2009
  35. 35. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is Thursday, November 12, 2009
  36. 36. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is undefined Thursday, November 12, 2009
  37. 37. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is undefined (It’s neither uphill, downhill, or level) Thursday, November 12, 2009
  38. 38. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. Thursday, November 12, 2009
  39. 39. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 Thursday, November 12, 2009
  40. 40. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 Down 2, right 1 Thursday, November 12, 2009
  41. 41. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  42. 42. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  43. 43. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  44. 44. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  45. 45. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  46. 46. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  47. 47. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  48. 48. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  49. 49. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  50. 50. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  51. 51. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  52. 52. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  53. 53. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  54. 54. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  55. 55. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  56. 56. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  57. 57. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 P Down 2, right 1 Thursday, November 12, 2009
  58. 58. Example 4 a. Find the slope of AB and CD for the given points. A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) Thursday, November 12, 2009
  59. 59. Example 4 a. Find the slope of AB and CD for the given points. A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) y 2 − y1 m (AB ) = x 2 − x1 Thursday, November 12, 2009
  60. 60. Example 4 a. Find the slope of AB and CD for the given points. A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) y 2 − y 1 2 − (−1) m (AB ) = = x 2 − x1 2−0 Thursday, November 12, 2009
  61. 61. Example 4 a. Find the slope of AB and CD for the given points. A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) y 2 − y 1 2 − (−1) 3 m (AB ) = = = x 2 − x1 2−0 2 Thursday, November 12, 2009
  62. 62. Example 4 a. Find the slope of AB and CD for the given points. A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) y 2 − y 1 2 − (−1) 3 m (AB ) = = = x 2 − x1 2−0 2 y 2 − y1 m (CD ) = x 2 − x1 Thursday, November 12, 2009
  63. 63. Example 4 a. Find the slope of AB and CD for the given points. A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) y 2 − y 1 2 − (−1) 3 m (AB ) = = = x 2 − x1 2−0 2 y 2 − y1 4 −1 m (CD ) = = x 2 − x 1 −1− (−3) Thursday, November 12, 2009
  64. 64. Example 4 a. Find the slope of AB and CD for the given points. A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) y 2 − y 1 2 − (−1) 3 m (AB ) = = = x 2 − x1 2−0 2 y 2 − y1 4 −1 3 m (CD ) = = = x 2 − x 1 −1− (−3) 2 Thursday, November 12, 2009
  65. 65. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) Thursday, November 12, 2009
  66. 66. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) A Thursday, November 12, 2009
  67. 67. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) B A Thursday, November 12, 2009
  68. 68. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) B C A Thursday, November 12, 2009
  69. 69. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) D B C A Thursday, November 12, 2009
  70. 70. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) D B C A Thursday, November 12, 2009
  71. 71. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) D B C A Thursday, November 12, 2009
  72. 72. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) D B The lines are parallel. C A Thursday, November 12, 2009
  73. 73. Example 4 b. Graph the t wo lines. What do you notice? A = (0, −1), B = (2, 2), C = (−3,1), D = (−1, 4) D B The lines are parallel. C A They have the same slope. Thursday, November 12, 2009
  74. 74. Homework Thursday, November 12, 2009
  75. 75. Homework p. 250 #1-35 odd “The power of imagination makes us infinite.” - John Muir Thursday, November 12, 2009

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