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# AA 3.2

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• ### AA 3.2

1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 11. 3.2 The Graph of y=mx+b Essential Question: How do we determine the slope and y-intercept of a line?
12. 12. 3 ways to Graph y = mx + b
13. 13. 3 ways to Graph y = mx + b make a table of values and plot the points
14. 14. 3 ways to Graph y = mx + b make a table of values and plot the points use a graphing calculator
15. 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. 16. y = 2x - 3 1st way: using a table x y
17. 17. y = 2x - 3 1st way: using a table x y 0
18. 18. y = 2x - 3 1st way: using a table x y 0 -3
19. 19. y = 2x - 3 1st way: using a table x y 0 -3
20. 20. y = 2x - 3 1st way: using a table x y 0 -3 1
21. 21. y = 2x - 3 1st way: using a table x y 0 -3 1 -1
22. 22. y = 2x - 3 1st way: using a table x y 0 -3 1 -1
23. 23. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2
24. 24. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2 1
25. 25. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2 1
26. 26. y = 2x - 3 1st way: using a table x y 0 -3 1 -1 2 1
27. 27. y = 2x - 3 2nd way: on the graphing calculator
28. 28. y = 2x - 3 2nd way: on the graphing calculator
29. 29. y = 2x - 3 2nd way: on the graphing calculator
30. 30. y = 2x - 3 2nd way: on the graphing calculator
31. 31. y = 2x - 3 3rd way: Use slope-intercept form
32. 32. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept:
33. 33. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3
34. 34. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3
35. 35. y = 2x - 3 3rd way: Use slope-intercept form * start at y-intercept: -3 * use slope to ﬁnd 2 more points
36. 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. 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. 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. 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. 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. 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. 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. 43. Note on Slope
44. 44. Note on Slope Positive Slope: rise from left to right
45. 45. Note on Slope Positive Slope: rise from left to right Negative Slope: fall from left to right
46. 46. 3y = 2x - 15
47. 47. 3y = 2x - 15 1st: Rewrite equation in slope intercept form
48. 48. 3y = 2x - 15 1st: Rewrite equation in slope intercept form y = 2/3 x - 5
49. 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. 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. 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. 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. 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. 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. 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. 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. 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. 58. Graph y = 3
59. 59. Graph y = 3 Horizontal Line
60. 60. Graph y = 3 Horizontal Line slope is
61. 61. Graph y = 3 Horizontal Line slope is 0
62. 62. Graph y = 3 Horizontal Line slope is 0 y-intercept is
63. 63. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3
64. 64. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3
65. 65. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3 DOMAIN: RANGE:
66. 66. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3 DOMAIN: all real numbers RANGE:
67. 67. Graph y = 3 Horizontal Line slope is 0 y-intercept is 3 DOMAIN: all real numbers RANGE: {3}
68. 68. Graph the following on the Calculator: y = 3x - 8 y = 3x
69. 69. Graph the following on the Calculator: y = 3x - 8 y = 3x
70. 70. Graph the following on the Calculator: y = 3x - 8 y = 3x
71. 71. Graph the following on the Calculator: y = 3x - 8 y = 3x What do you notice?
72. 72. Graph the following on the Calculator: y = 3x - 8 y = 3x What do you notice? parallel lines
73. 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. 74. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES?
75. 75. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES? table
76. 76. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES? table graphing calculator
77. 77. SUMMARY WHAT ARE THREE WAYS TO GRAPH LINES? table graphing calculator slope-intercept form - using m and b
78. 78. Homework: page 149 #1-24