Integrated 2 Section 6-3

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Write and Graph Equations

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  • Integrated 2 Section 6-3

    1. 1. SECTION 6-3 Write and Graph Equations
    2. 2. ESSENTIAL QUESTIONS How do you write equations of lines using slope, intercepts, and points? How do you graph a line given the equation? Where you’ll see this: Finance, sports, transportation, recreation
    3. 3. VOCABULARY 1. Linear Equation: 2. y-intercept: 3. Slope-intercept Form: 4. Point-slope form:
    4. 4. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: 3. Slope-intercept Form: 4. Point-slope form:
    5. 5. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis 3. Slope-intercept Form: 4. Point-slope form:
    6. 6. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis (It’s a point!) 3. Slope-intercept Form: 4. Point-slope form:
    7. 7. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis (It’s a point!) 3. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept 4. Point-slope form:
    8. 8. VOCABULARY 1. Linear Equation: An equation whose graph is a line 2. y-intercept: The point where the graph crosses the y-axis (It’s a point!) 3. Slope-intercept Form: y = mx + b, where m = slope and b = y coordinate of the y-intercept 4. Point-slope form: y - y1 = m(x - x1), where m = slope and (x1, y1) is a point on the line
    9. 9. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. 1 a. y = x 2
    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
    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
    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)
    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)
    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)
    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)
    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)
    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)
    18. 18. 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)
    19. 19. 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)
    20. 20. 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)
    21. 21. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6
    22. 22. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x
    23. 23. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x
    24. 24. EXAMPLE 1 Identify the slope and y-intercept for each line and graph the lines. b. 2y − x = −6 +x +x
    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
    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
    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
    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= 2
    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) 2
    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) 2
    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) 2
    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) 2
    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) 2
    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) 2
    35. 35. 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) 2
    36. 36. 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) 2
    37. 37. 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) 2
    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)
    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
    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
    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 + 4
    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 + 4
    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 + 4
    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 + 4
    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 + 4
    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 + 4
    47. 47. 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 + 4
    48. 48. 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 + 4
    49. 49. 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 + 4
    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)
    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
    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 )
    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 ) 3 y + 2 = (x − 8) 4
    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 ) 3 y + 2 = (x − 8) 4 3 y +2= x−6 4
    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 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
    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 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
    57. 57. 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 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
    58. 58. 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 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
    59. 59. 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 ) 3 y + 2 = (x − 8) 4 3 3 y +2= x−6 4 y = x−8 4
    60. 60. EXAMPLE 3 Write the equation for the line. a.
    61. 61. EXAMPLE 3 Write the equation for the line. a. 5 m=− 7
    62. 62. EXAMPLE 3 Write the equation for the line. a. 5 m=− (4, -1) 7
    63. 63. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 m=− (4, -1) 7
    64. 64. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 y +1= − (x − 4) 7 5 m=− (4, -1) 7
    65. 65. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 y +1= − (x − 4) 7 5 20 y +1= − x + 7 7 5 m=− (4, -1) 7
    66. 66. EXAMPLE 3 Write the equation for the line. a. y − y1 = m(x − x1 ) 5 y +1= − (x − 4) 7 5 20 y +1= − x + 7 7 5 13 5 y=− x+ 7 7 m=− (4, -1) 7
    67. 67. EXAMPLE 3 Write the equation for the line. b.
    68. 68. EXAMPLE 3 Write the equation for the line. b. 6 m= 8
    69. 69. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = 8 4
    70. 70. EXAMPLE 3 Write the equation for the line. b. 6 3 m= = (3, 2) 8 4
    71. 71. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 6 3 m= = (3, 2) 8 4
    72. 72. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 3 y − 2 = (x − 3) 4 6 3 m= = (3, 2) 8 4
    73. 73. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 3 y − 2 = (x − 3) 4 3 9 y−2= x− 4 4 6 3 m= = (3, 2) 8 4
    74. 74. EXAMPLE 3 Write the equation for the line. b. y − y1 = m(x − x1 ) 3 y − 2 = (x − 3) 4 3 9 y−2= x− 4 4 3 1 6 3 y= x− 4 4 m= = (3, 2) 8 4
    75. 75. HOMEWORK
    76. 76. HOMEWORK p. 256 #1-33 odd, 34 “We can have facts without thinking, but we cannot have thinking without facts.” - John Dewey

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