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Geometry Section 3-4 1112
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Geometry Section 3-4 1112

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Equations of Lines

Equations of Lines

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  • 1. SECTION 3-4 Equations of LinesTuesday, January 3, 2012
  • 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. VOCABULARY 1. Slope-intercept Form: 2. Point-slope form:Tuesday, January 3, 2012
  • 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. 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. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2Tuesday, January 3, 2012
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6Tuesday, January 3, 2012
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. EXAMPLE 3 Write the equation for the line. a.Tuesday, January 3, 2012
  • 58. EXAMPLE 3 Write the equation for the line. a. 5 m=− 7Tuesday, January 3, 2012
  • 59. EXAMPLE 3 Write the equation for the line. a. 5 m=− (4, -1) 7Tuesday, January 3, 2012
  • 60. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 m=− (4, -1) 7Tuesday, January 3, 2012
  • 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. 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. 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. EXAMPLE 3 Write the equation for the line. b.Tuesday, January 3, 2012
  • 65. EXAMPLE 3 Write the equation for the line. b. 6 m= 8Tuesday, January 3, 2012
  • 66. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = 8 4Tuesday, January 3, 2012
  • 67. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = (3, 2) 8 4Tuesday, January 3, 2012
  • 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. 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. 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. 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. CHECK YOUR UNDERSTANDING Review problems #1-12 on p. 200Tuesday, January 3, 2012
  • 73. PROBLEM SETTuesday, January 3, 2012
  • 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