1. By Lia Servidio and Kelly Lively
Slope
By Lia Servidio and Kelly Lively

2. What is Slope? Slope is a measure of how steep a line is
The greater the slope value, the steeper the line

3. Slope Formula Slope is generally represented as the letter m
Equal to the change in the y-coordinates divided by the change in the x-coordinates

4. How to Find Slope From Two Points
Identify the two points: (x1,y1) and (x2,y2)
Use the formula m=(y2-y1)/(x2-x1)
*It does not matter which set of coordinates are considered to be (x1,y1) and which are considered to be (x2,y2)

5. Example What is the slope between the points (-2,5) and (6,10)?
If (x1,y1)=(-2,5) and (x2,y2)=(6,10)
If (x1,y1)=(6,10) and (x2,y2)=(-2,5)

6. How to Find Slope From an Equation
*Slope is equal to m in the equation y=mx+b
Set the equation equal to y (if not already)
Slope is equal to the constant in front of x

7. Examples What is the slope of the line y=4x+7?
Since the equation is already set equal to y, look for the constant next to the x.
y=4x+7, m=4
What is the slope of the line 6x+3y=12?
Set the equation equal to y: 3y=-6x+12
y=-2x+4
Look for the constant next to the x, m=-2

8. How to Find Slope Using a Graph

9. Horizontal and Vertical Lines
The slope of a horizontal line is 0 because there is no change in y
The slope of a vertical line is undefined because it is impossible to divide by 0 and there is no change in x

10. Welcome to Who Wants to be a Millionaire
50:50 15
$1 Million 14
$500,000
Welcome to Who Wants to be a Millionaire 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

11. Another Presentation © 2002 - All rights Reserved Mark E. Damon

13. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

14. Find the slope of the line through the pair of points:15
$1 Million 14
$500,000 13
$250,000
Find the slope of the line through the pair of points:
(-4,7),(-6,-4) 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: -11/2
B: 11/2
C: -1
D: 2/11

15. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

16. Find the slope: y=-5x-7 15 $1 Million 14 $500,000 13 $250,000 12
$125,000
Find the slope:
y=-5x-7 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 5/7
B: 5
C: -7
D: -5

17. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

18. Find the slope of the line through the pair of points:15
$1 Million 14
$500,000
Find the slope of the line through the pair of points:
(19,3),(2,3) 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 0
B: 1
C: -1
D: Undefined

19. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

20. Find the slope: 15 $1 Million 14 $500,000 13 $250,000 12 $125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 2/3
B: 3/2
C: - 1/2
D: 2

21. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

22. Find the slope of the line through the pair of points:15
$1 Million 14
$500,000 13
$250,000
Find the slope of the line through the pair of points:
(17,-13),(17,8) 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 0
B: 1
C: Undefined
D: -1

23. You’ve Reached the $1,000 Milestone! Congratulations! Congratulations!

24. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

25. Find the slope: 8x+3y=-9 15 $1 Million 14 $500,000 13 $250,000 12
$125,000
Find the slope:
8x+3y=-9 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 9/8
B: -8/3
C: 3/8
D: -1/3

26. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

27. What is the slope of this line?15
$1 Million
What is the slope of this line? 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 3/2
B: Undefined
C: 1
D: 0

28. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

29. Find the slope: x=-1 15 $1 Million 14 $500,000 13 $250,000 12 $125,00011
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: Undefined
B: 0
C: 1
D: -1

30. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

31. What letter is commonly used to represent slope?15
$1 Million 14
$500,000 13
$250,000 12
$125,000
What letter is commonly used to represent slope? 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: k
B: x
C: m
D: y

32. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

33. Which is not equal to slope?15
$1 Million 14
$500,000 13
$250,000 12
$125,000
Which is not equal to slope? 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: Rise/Run
B: (y2-y1)/(x2-x1)
C: ΔY/ ΔX
D: Run/Rise

34. You’ve Reached the $32,000 Milestone! Congratulations!

35. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

36. How would you describe the slope?15
$1 Million 14
$500,000
How would you describe the slope? 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: Positive
B: Negative
C: Zero
D: Undefined

37. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

38. The slope of a vertical line is:15
$1 Million 14
$500,000 13
$250,000 12
$125,000
The slope of a vertical line is: 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 1
B: -1
C: Undefined
D: 0

39. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

40. The slope of a horizontal line is:15
$1 Million 14
$500,000 13
$250,000 12
$125,000
The slope of a horizontal line is: 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: Undefined
B: 1
C: Depends on points used to calculate it
D: 0

41. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

42. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000
Find the slope of the line passing through the points (-3,5) and (-3,7) 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: Undefined
B: -2/3
C: 2/3
D: 0

43. 15
$1 Million 14
$500,000 13
$250,000 12
$125,000 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200 1
$100

44. What is the slope of the equation 1/2x + 2y = 3?15
$1 Million 14
$500,000 13
$250,000 12
$125,000
What is the slope of the equation /2x + 2y = 3? 11
$64,000 10
$32,000 9
$16,000 8
$8,000 7
$4,000 6
$2,000 5
$1,000 4
$500 3
$300 2
$200
50:50 1
$100
A: 3/2
B: -1/4
C: 2
D: 1/2

45. YOU WIN $1 MILLION DOLLARS!