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# 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