1. Graphing Motion
The Slope of a Line

2. Important Vocabulary Terms
The slope of a line is the ratio of the vertical rise to the
horizontal run between any two points on the line.
You can describe steepness by using slope of a line.

3. The Slope Ratio vertical rise slope = horizontal run so 10 slope = = 25
Slope does not
have units
horizontal run = 5

4. Let’s Try It Out!
Let’s try and find the slope of a hill that has a vertical rise of 40ft and
a horizontal run of 200ft. Let m represent the slope.
vertical
rise = 40 ft
horizontal run = 200 ft S
Click the green solution
button to check work.

5. Solution: Apply the formula- vertical rise to horizontal run
Vertical rise = 40 ft
40 ft. 1 5 = =
0.2
200 ft.
Horizontal run = 200 ft
The slope of the hill is
0.2
back
forward

6. . . How to find the rise and the run (x2, y2) y2 - y1 (x1, y1) x2 - x1
The slope m of a line that passes through
the points (x1, y1) and (x2, y2) is
m =
rise
run =
change in y
change in x
y2 - y1
x2 - x1

7. HOW TO DETERMINE SLOPE
run
rise
slope = 1/3.24
run
rise
slope = 1/3.24

8. Different Types of Slope
1. Positive Slope
A line that rises from left to right
A line falls from left to right
2. Negative Slope
3. Zero Slope
A line is horizontal

9. . . Problem # 1 (x , y ) = (1, 0) and (x , y ) = (3, 4) m = y - x m =2 1 3 5 7 y -1
m = y 2 1 - x .
m =
4 - 0
3 - 1 .
m = 4 2
The slope of the line is 2

10. . . Problem # 2 (x , y ) = (0, 9) and (x , y ) = (4, 7) m = y - x m =1
= (0, 9) and
(x , y ) = (4, 7) 2 . . 1 3 5 7 y -1
m = y 2 1 - x
m =
7 - 9
4 - 0
m = -2 4 or -1 2
The slope of the line is -1 which makes it
a negative slope. 2

11. Problem # 3 m = y - x m = y - x m = 15 - 10 3 - 2 m = 25 - 5 5 - 1 m =
(1,5), (2,10), (3,15), (4,20), (5,25)
m = y 2 1 - x
m = y 2 1 - x
m =
3 - 2
m =
25 - 5
5 - 1
m = 5 1 or
m = 20 5 or

12. Problem # 4 m = y - x m = y - x m = 60 - 40 5 - 4 m = 15 - 5 2 - 1 m =
(1,5), (2,15), (3,25), (4,40), (5,60)
Seconds 4-5
m = y 2 1 - x
m = y 2 1 - x
Seconds 1-2
m =
5 - 4
m =
15 - 5
2 - 1
m = 20 1 or
m = 10 2 or 5
The slope of this line is changing. The object is speeding up

13. SLOPE AND SPEED
1. Who is walking faster during the first 2 seconds?
Answer: Cory. The slope and thus speed is 6/2 = 3 m/s. Notice Cory’s line is steeper at that segment than the other lines.
run
rise

14. SLOPE AND SPEED
2. Who is walking faster the last 3 seconds?
Answer: Justin. The slope and thus speed is 6/3 = 2 m/s. Notice Justin’s line is steeper at that segment than the other lines. Cory is now the slowest (least steep slope.
run
rise

15. SLOPE AND SPEED
1. What is happening to the slope/speed as the coaster cars go up an incline?
Answer: The slope gets less steep, and thus the speed decreases. You know that when you go uphill you become slower because you are going against the force of gravity.
Less steep slope: lower speed
Very steep slope: high speed

16. SLOPE AND SPEED
2. What is happening to the slope/speed as the coaster cars go down a decline?
Answer: The slope gets more steep, and thus the speed increases. You know that when you go downhill you become faster because you are going with the force of gravity.
more steep slope: higher speed
Less steep slope: lower speed

17. SLOPE AND SPEED
3. What is happening to the slope/speed as the coaster cars goes along a straightaway?
Answer: The slope stays the same, and thus the speed stays the same (constant speed).
Same slope (doesn’t change): constant speed

18. What type of motion?
constant speed

19. What type of motion?
positive acceleration

20. What type of motion?
negative acceleration

21. What type of motion?
-constant speed
-0 speed

22. Fastest Speed?
green, because
it has the highest
slope

23. What type of motion?
negative acceleration

24. What type of motion?
positive acceleration