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AA 3.2

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    • 1. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y €
    • 2. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y €
    • 3. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 y = 3x - 4 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y €
    • 4. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 900y = 100x + 1000 y = 3x - 4 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y €
    • 5. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 900y = 100x + 1000 y = 3x - 4 y = 1/9 x + 10/9 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y €
    • 6. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 900y = 100x + 1000 y = 3x - 4 y = 1/9 x + 10/9 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y 6x + 4y = 3 + 12x €
    • 7. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 900y = 100x + 1000 y = 3x - 4 y = 1/9 x + 10/9 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y 6x + 4y = 3 + 12x € 4y = 6x + 3
    • 8. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 900y = 100x + 1000 y = 3x - 4 y = 1/9 x + 10/9 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y 6x + 4y = 3 + 12x € 4y = 6x + 3 y = 3/2 x + 3/4
    • 9. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 900y = 100x + 1000 y = 3x - 4 y = 1/9 x + 10/9 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y 6x + 4y = 3 + 12x -2y = x € 4y = 6x + 3 y = 3/2 x + 3/4
    • 10. Warm-Up: Solve for y. 1. 3y = 9x - 12 2. 200x + 500y = 300x - 400y + 1000 divide both sides by 3 900y = 100x + 1000 y = 3x - 4 y = 1/9 x + 10/9 1 1 1 3. 2 x+ y= + x 3 4 4. 2x - y = 3x + y 6x + 4y = 3 + 12x -2y = x € 4y = 6x + 3 y = -1/2 x y = 3/2 x + 3/4
    • 11. 3.2 The Graph of y=mx+b Essential Question: How do we determine the slope and y-intercept of a line?
    • 12. 3 ways to Graph y = mx + b
    • 13. 3 ways to Graph y = mx + b make a table of values and plot the points
    • 14. 3 ways to Graph y = mx + b make a table of values and plot the points use a graphing calculator
    • 15. 3 ways to Graph y = mx + b make a table of values and plot the points use a graphing calculator use slope and y-intercept to draw line
    • 16. y = 2x - 3 1st way: using a table x y
    • 17. y = 2x - 3 1st way: using a table x y 0
    • 18. y = 2x - 3 1st way: using a table x y 0 -3
    • 19. y = 2x - 3 1st way: using a table x y 0 -3
    • 20. y = 2x - 3 1st way: using a table x y 0 -3 1
    • 21. y = 2x - 3 1st way: using a table x y 0 -3 1 -1
    • 22. y = 2x - 3 1st way: using a table x y 0 -3 1 -1
    • 23. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2
    • 24. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2 1
    • 25. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2 1
    • 26. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2 1
    • 27. y = 2x - 3 2nd way: on the graphing calculator
    • 28. y = 2x - 3 2nd way: on the graphing calculator
    • 29. y = 2x - 3 2nd way: on the graphing calculator
    • 30. y = 2x - 3 2nd way: on the graphing calculator
    • 31. y = 2x - 3 3rd way: Use slope-intercept form
    • 32. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept:
    • 33. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3
    • 34. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3
    • 35. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points
    • 36. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points m = 2 or 2/1
    • 37. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points m = 2 or 2/1 rise 2 run 1
    • 38. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points m = 2 or 2/1 rise 2 run 1 up 2 right 1 OR down 2 left 1
    • 39. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points m = 2 or 2/1 rise 2 run 1 up 2 right 1 OR down 2 left 1
    • 40. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points m = 2 or 2/1 rise 2 run 1 up 2 right 1 OR down 2 left 1
    • 41. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points m = 2 or 2/1 rise 2 run 1 up 2 right 1 OR down 2 left 1 * connect the dots
    • 42. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to find 2 more points m = 2 or 2/1 rise 2 run 1 up 2 right 1 OR down 2 left 1 * connect the dots
    • 43. Note on Slope
    • 44. Note on Slope Positive Slope: rise from left to right
    • 45. Note on Slope Positive Slope: rise from left to right Negative Slope: fall from left to right
    • 46. 3y = 2x - 15
    • 47. 3y = 2x - 15 1st: Rewrite equation in slope intercept form
    • 48. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5
    • 49. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form
    • 50. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5
    • 51. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5
    • 52. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5 m = 2/3
    • 53. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5 m = 2/3 up 2 right 3 OR down 2 left 3
    • 54. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5 m = 2/3 up 2 right 3 OR down 2 left 3
    • 55. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5 m = 2/3 up 2 right 3 OR down 2 left 3
    • 56. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5 m = 2/3 up 2 right 3 OR down 2 left 3 3rd: Connect the dots
    • 57. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5 2nd: Graph the line using a table or slope-intercept form b = -5 m = 2/3 up 2 right 3 OR down 2 left 3 3rd: Connect the dots
    • 58. Graph y = 3
    • 59. Graph y = 3 Horizontal Line
    • 60. Graph y = 3 Horizontal Line slope is
    • 61. Graph y = 3 Horizontal Line slope is 0
    • 62. Graph y = 3 Horizontal Line slope is 0 y-intercept is
    • 63. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3
    • 64. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3
    • 65. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3 DOMAIN: RANGE:
    • 66. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3 DOMAIN: all real numbers RANGE:
    • 67. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3 DOMAIN: all real numbers RANGE: {3}
    • 68. Graph the following on the Calculator: y = 3x - 8 y = 3x
    • 69. Graph the following on the Calculator: y = 3x - 8 y = 3x
    • 70. Graph the following on the Calculator: y = 3x - 8 y = 3x
    • 71. Graph the following on the Calculator: y = 3x - 8 y = 3x What do you notice?
    • 72. Graph the following on the Calculator: y = 3x - 8 y = 3x What do you notice? parallel lines
    • 73. Graph the following on the Calculator: y = 3x - 8 y = 3x What do you notice? parallel lines PARALLEL LINES have the SAME SLOPE
    • 74. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES?
    • 75. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES? table
    • 76. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES? table graphing calculator
    • 77. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES? table graphing calculator slope-intercept form - using m and b
    • 78. Homework: page 149 #1-24

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