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# Geometry Section 3-4 1112

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Equations of Lines

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### Geometry Section 3-4 1112

1. 1. SECTION 3-4 Equations of LinesTuesday, January 3, 2012
2. 2. ESSENTIAL QUESTIONS How do you write an equation of a line given information about the graph? How do you solve problems by writing equations?Tuesday, January 3, 2012
3. 3. VOCABULARY 1. Slope-intercept Form: 2. Point-slope form:Tuesday, January 3, 2012
4. 4. VOCABULARY 1. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept -- (0, b) 2. Point-slope form:Tuesday, January 3, 2012
5. 5. VOCABULARY 1. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept -- (0, b) 2. Point-slope form: y - y1 = m(x - x1), where m = slope and (x1, y1) is a point on the lineTuesday, January 3, 2012
6. 6. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2Tuesday, January 3, 2012
7. 7. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2Tuesday, January 3, 2012
8. 8. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0Tuesday, January 3, 2012
9. 9. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
10. 10. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
11. 11. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
12. 12. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
13. 13. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
14. 14. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
15. 15. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
16. 16. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
17. 17. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2 1 m= 2 b=0 y-intercept: (0, 0)Tuesday, January 3, 2012
18. 18. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6Tuesday, January 3, 2012
19. 19. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +xTuesday, January 3, 2012
20. 20. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +xTuesday, January 3, 2012
21. 21. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +xTuesday, January 3, 2012
22. 22. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6Tuesday, January 3, 2012
23. 23. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2Tuesday, January 3, 2012
24. 24. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2Tuesday, January 3, 2012
25. 25. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= 2Tuesday, January 3, 2012
26. 26. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
27. 27. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
28. 28. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
29. 29. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
30. 30. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
31. 31. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
32. 32. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
33. 33. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
34. 34. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x 2y = x − 6 2 2 1 y = x −3 2 1 m= y-intercept = (0, -3) 2Tuesday, January 3, 2012
35. 35. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4)Tuesday, January 3, 2012
36. 36. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-interceptTuesday, January 3, 2012
37. 37. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + bTuesday, January 3, 2012
38. 38. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
39. 39. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
40. 40. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
41. 41. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
42. 42. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
43. 43. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
44. 44. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
45. 45. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
46. 46. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. a. m = -2, (0, 4) Use slope-intercept y = mx + b y = −2x + 4Tuesday, January 3, 2012
47. 47. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2)Tuesday, January 3, 2012
48. 48. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slopeTuesday, January 3, 2012
49. 49. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 )Tuesday, January 3, 2012
50. 50. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) y + 2 = (x − 8) 3 4Tuesday, January 3, 2012
51. 51. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) y + 2 = (x − 8) 3 4 y +2= x−6 3 4Tuesday, January 3, 2012
52. 52. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) y + 2 = (x − 8) 3 4 y +2= x−6 3 4 y = x−8 3 4Tuesday, January 3, 2012
53. 53. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) y + 2 = (x − 8) 3 4 y +2= x−6 3 4 y = x−8 3 4Tuesday, January 3, 2012
54. 54. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) y + 2 = (x − 8) 3 4 y +2= x−6 3 4 y = x−8 3 4Tuesday, January 3, 2012
55. 55. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) y + 2 = (x − 8) 3 4 y +2= x−6 3 4 y = x−8 3 4Tuesday, January 3, 2012
56. 56. EXAMPLE 2 Write the equation of the line, choosing which form you would need before you begin. Then graph the line. b. m = 3/4, (8, -2) Use point-slope y − y1 = m(x − x1 ) y + 2 = (x − 8) 3 4 y +2= x−6 3 4 y = x−8 3 4Tuesday, January 3, 2012
57. 57. EXAMPLE 3 Write the equation for the line. a.Tuesday, January 3, 2012
58. 58. EXAMPLE 3 Write the equation for the line. a. 5 m=− 7Tuesday, January 3, 2012
59. 59. EXAMPLE 3 Write the equation for the line. a. 5 m=− (4, -1) 7Tuesday, January 3, 2012
60. 60. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 m=− (4, -1) 7Tuesday, January 3, 2012
61. 61. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) y +1= − (x − 4) 5 7 5 m=− (4, -1) 7Tuesday, January 3, 2012
62. 62. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) y +1= − (x − 4) 5 7 y +1= − x + 5 7 20 7 5 m=− (4, -1) 7Tuesday, January 3, 2012
63. 63. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) y +1= − (x − 4) 5 7 y +1= − x + 5 7 20 7 5 y=− x+ 5 7 13 7 m=− (4, -1) 7Tuesday, January 3, 2012
64. 64. EXAMPLE 3 Write the equation for the line. b.Tuesday, January 3, 2012
65. 65. EXAMPLE 3 Write the equation for the line. b. 6 m= 8Tuesday, January 3, 2012
66. 66. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = 8 4Tuesday, January 3, 2012
67. 67. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = (3, 2) 8 4Tuesday, January 3, 2012
68. 68. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 6 3 m= = (3, 2) 8 4Tuesday, January 3, 2012
69. 69. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) y − 2 = (x − 3) 3 4 6 3 m= = (3, 2) 8 4Tuesday, January 3, 2012
70. 70. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) y − 2 = (x − 3) 3 4 y−2= x− 3 4 9 4 6 3 m= = (3, 2) 8 4Tuesday, January 3, 2012
71. 71. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) y − 2 = (x − 3) 3 4 y−2= x− 3 4 9 4 6 3 y= x− 3 4 1 4 m= = (3, 2) 8 4Tuesday, January 3, 2012
72. 72. CHECK YOUR UNDERSTANDING Review problems #1-12 on p. 200Tuesday, January 3, 2012
73. 73. PROBLEM SETTuesday, January 3, 2012
74. 74. PROBLEM SET p. 200 #13-41 odd, 55 “We can have facts without thinking, but we cannot have thinking without facts.” - John DeweyTuesday, January 3, 2012