The Graph of y = mx + b

1. Section 3-2
The Graph of y = mx + b

2. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y

3. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
y = 3x - 4
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y

4. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y

5. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y

6. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y

7. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
y = 9x + 9
1 10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y

8. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
y = 9x + 9
1 10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y
12 ( 1
2
1
)
x + 3 y = 12 ( 1
4
+x )

9. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
y = 9x + 9
1 10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y
12 ( 1
2 )
x + 3 y = 12 4 + x
1
(1
)
6x+4y=3+12x

10. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
y = 9x + 9
1 10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y
12 ( 1
2 )
x + 3 y = 12 4 + x
1
(1
)
6x+4y=3+12x
4y=6x+3

11. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
y = 9x + 9
1 10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y
12 ( 1
2 )
x + 3 y = 12 4 + x
1
(1
)
6x+4y=3+12x
4y=6x+3
y= x+
3
2
3
4

12. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
y = 9x + 9
1 10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y
12 ( 1
2
1
) (
x + 3 y = 12 4 + x
1
) -2y=x
6x+4y=3+12x
4y=6x+3
y= x+
3
2
3
4

13. Warm-up
Solve for y.
1. 3y=9x − 12 2. 200x+500y=300x-400y+1000
-200x+400y -200x+400y
y = 3x - 4
900y = 100x+1000
9y=x+10
y = 9x + 9
1 10
3. 1
2
x + y = +x
1
3
1
4 4. 2x-y=3x+y
12 ( 1
2
1
) (
x + 3 y = 12 4 + x
1
) -2y=x
6x+4y=3+12x y =− x
1
2
4y=6x+3
y= x+
3
2
3
4

14. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3

15. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3
m=2

16. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3
m=2
y-int. = (0, -3)

17. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3
m=2 m = -2/3
y-int. = (0, -3)

18. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3
m=2 m = -2/3
y-int. = (0, -3) y-int. = (0, 1)

19. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3
m=2 m = -2/3
y-int. = (0, -3) y-int. = (0, 1)

20. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3
m=2 m = -2/3
y-int. = (0, -3) y-int. = (0, 1)

21. Example 1
State the slope and y-intercept of each line and graph them.
Check your graphs by using your graphing calculator.
1. y = 2x -3 2. y = − x + 1
2
3
m=2 m = -2/3
y-int. = (0, -3) y-int. = (0, 1)

22. Example 2
Graph 3y = 2x - 15.

23. Example 2
Graph 3y = 2x - 15.
3y = 2x - 15

24. Example 2
Graph 3y = 2x - 15.
3y = 2x - 15
3 3

25. Example 2
Graph 3y = 2x - 15.
3y = 2x - 15
3 3
y = 2/3 x - 5

26. Example 2
Graph 3y = 2x - 15.
3y = 2x - 15
3 3
y = 2/3 x - 5

27. Equation for a horizontal line:

28. Equation for a horizontal line: y = c, where c is a constant

29. Equation for a horizontal line: y = c, where c is a constant
Equation for a vertical line:

30. Equation for a horizontal line: y = c, where c is a constant
Equation for a vertical line: x = c, where c is a constant

31. Example 3
Graph y = -4 and x = 2

32. Example 3
Graph y = -4 and x = 2

33. Example 3
Graph y = -4 and x = 2
How did we do this?

34. Example 3
Graph y = -4 and x = 2
How did we do this?

35. Example 3
Graph y = -4 and x = 2
How did we do this?
2nd DRAW
(PRGM)

36. Example 3
Graph y = -4 and x = 2
How did we do this?
2nd DRAW
(PRGM)

37. Example 3
Graph y = -4 and x = 2
How did we do this?
2nd DRAW
(PRGM)

38. Example 4
Graph y = 2/3 x - 2 and y = 2/3 x + 3.

39. Example 4
Graph y = 2/3 x - 2 and y = 2/3 x + 3.

40. Theorems

41. Theorems
1. If t wo lines have the same slope, then they are parallel

42. Theorems
1. If t wo lines have the same slope, then they are parallel
2. If t wo lines are parallel, then they have the same slope

43. Theorems
1. If t wo lines have the same slope, then they are parallel
2. If t wo lines are parallel, then they have the same slope
(It’s biconditional)

44. Homework

45. Homework
p. 149 #1 - 24
“The idea of perfect closes your mind to new standards. When
you drive hard toward one ideal, you miss opportunities and
paths, not to mention hurting your confidence. Believe in your
potential and then go out and explore it; don’t limit it.”
- John Eliot, Ph.D.