Int Math 2 Section 6-1 1011

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Slope of a Line

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  • Int Math 2 Section 6-1 1011

    1. 1. Section 6-2 Slope of a Line
    2. 2. Essential QuestionsHow do you find the slope of a line?How do you identify horizontal andvertical lines?Where you’ll see it: Business, science, transportation
    3. 3. Vocabulary1. Slope:
    4. 4. Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change
    5. 5. Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again.
    6. 6. Vocabulary1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again.1. Slope:
    7. 7. Vocabulary1. 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”
    8. 8. Vocabulary1. 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:
    9. 9. Vocabulary1. 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
    10. 10. MATH CALISTHENICS!
    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)
    12. 12. Example 1 Graph the line the goes through the given points, then find the slope of the line.C = (−4,0) CD = (4, 4)
    13. 13. Example 1 Graph the line the goes through the given points, then find the slope of the line. DC = (−4,0) CD = (4, 4)
    14. 14. Example 1 Graph the line the goes through the given points, then find the slope of the line. DC = (−4,0) CD = (4, 4)
    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 − x1C = (−4,0) CD = (4, 4)
    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 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4)
    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 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4) 4 = 8
    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 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4) 4 1 = = 8 2
    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 − x1C = (−4,0) C 4−0 =D = (4, 4) 4 − (−4) 4 1 = = 8 2 Here, the slope tells us “Up 1, Right 2”
    20. 20. Example 2Find the slope for the line containing the following: a. (9, -2), (3, -2) b. (3, 12), (3, -4)
    21. 21. Example 2Find 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
    22. 22. Example 2Find 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
    23. 23. Example 2Find 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
    24. 24. Example 2Find 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
    25. 25. Example 2Find 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
    26. 26. Example 2Find 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
    27. 27. Example 2Find 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 − 1 2 = = 3 −9 3 −3 0 = =0 −6 Horizontal
    28. 28. Example 2Find 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 − 1 2 = = 3 −9 3 −3 0 −1 6 = =0 = −6 0 Horizontal
    29. 29. Example 2Find 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 − 1 2 = = 3 −9 3 −3 0 −1 6 = =0 = Undefined −6 0 Horizontal
    30. 30. Example 2Find 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 − 1 2 = = 3 −9 3 −3 0 −1 6 = =0 = Undefined −6 0 Horizontal Vertical
    31. 31. Horizontal vs. Vertical
    32. 32. Horizontal vs. Vertical Horizontal lines have slopes of
    33. 33. Horizontal vs. Vertical Horizontal lines have slopes of zero
    34. 34. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”)
    35. 35. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is
    36. 36. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is undefined
    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)
    38. 38. Example 3Graph the line that passes through P = (-1, 1) and has a slope of -2.
    39. 39. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2−2 = 1
    40. 40. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1Down 2, right 1
    41. 41. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    42. 42. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    43. 43. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    44. 44. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    45. 45. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    46. 46. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    47. 47. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    48. 48. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    49. 49. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    50. 50. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    51. 51. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    52. 52. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    53. 53. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    54. 54. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    55. 55. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    56. 56. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    57. 57. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. −2 −2 = 1 PDown 2, right 1
    58. 58. Example 4a. Find the slope of AB and CD for the given points. A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4)
    59. 59. Example 4a. 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
    60. 60. Example 4a. 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
    61. 61. Example 4a. 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
    62. 62. Example 4a. 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
    63. 63. Example 4a. 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)
    64. 64. Example 4a. 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
    65. 65. Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4)
    66. 66. Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) A
    67. 67. Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) B A
    68. 68. Example 4b. Graph the t wo lines. What do you notice?A = (0 , −1 ), B = (2, 2), C = (−3 ,1 ), D = (−1 , 4) B C A
    69. 69. Example 4b. 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
    70. 70. Example 4b. 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
    71. 71. Example 4b. 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
    72. 72. Example 4b. 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
    73. 73. Example 4b. 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.
    74. 74. Problem Set
    75. 75. Problem Set p. 250 #1-35 odd“The power of imagination makes us infinite.” - John Muir

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