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Integrated Math 2 Section 6-2

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    Integrated Math 2 Section 6-2 - Presentation Transcript

    1. Section 6-2 Slope of a Line Thursday, November 12, 2009
    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. Vocabulary 1. Slope: Thursday, November 12, 2009
    4. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Thursday, November 12, 2009
    5. Vocabulary 1. Slope: The ratio of vertical distance change to horizontal distance change Let’s try again. Thursday, November 12, 2009
    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. 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. 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. 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. MATH CALISTHENICS! Thursday, November 12, 2009
    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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Horizontal vs. Vertical Thursday, November 12, 2009
    32. Horizontal vs. Vertical Horizontal lines have slopes of Thursday, November 12, 2009
    33. Horizontal vs. Vertical Horizontal lines have slopes of zero Thursday, November 12, 2009
    34. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Thursday, November 12, 2009
    35. Horizontal vs. Vertical Horizontal lines have slopes of zero (Think “horizon”) Vertical lines have a slope that is Thursday, November 12, 2009
    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. 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. Example 3 Graph the line that passes through P = (-1, 1) and has a slope of -2. Thursday, November 12, 2009
    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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Homework Thursday, November 12, 2009
    75. Homework p. 250 #1-35 odd “The power of imagination makes us infinite.” - John Muir Thursday, November 12, 2009
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    Slope of a Line

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