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