1. Learning Goal
I can determine the rate of change of relationships from a graph or diagram that represents the situation

2. Rates of Change are seen everywhere.

3. The rate of change of the roof of a house is referred to as the pitch of the roof by home builders.

4. Give one reason why some homes have roofs which have a greater pitch.
There is less snow build up in the wintertime.

5. Engineers refer to the rate of change of a road as the grade.

6. They often refer to the grade as a percentage.

7. Rates of Change (Slopes) of lines
rise
run
Rate of change = slope = m =
The rate of change of a line is the steepness of the line.

8. 8
100
A grade of 8% would mean for every run of 100 units, there is a rise of 8 units.
Slope =
= 8%

9. The steepness of wheelchair ramps is of great importance to handicapped persons.1 12
The rate of change of wheelchair ramps is usually about …?
The slope of wheelchair ramps is usually about 1/12.
If the rise is 1.5 m, what is the run?
Ans: 18 m

10. Determine the rate of change of the line.
5 cm
9 cm
We use the letter m because in French the word for “to go up” is monter.
Because the rate of change is a ratio, there are no units such as cm or cm2.

11. Determine the rate of change (pitch) of the roof.

12. Determine the rate of change of the staircase.2 3 3 3

13. Determine the rate of change.12 10 9 3 8 6 4
Confirm with the class that other points on the line besides (4,6) and (13,9) would also have given slope 1/3. 2 2 4 6 8 10 12 14

14. Determine the rate of change.12 10
– 5 8 6 7 4
A student may ask about the possibility of seeing the upward/positive rise from (11,5) to (4,10) as 5. Confirm that this is correct, but would generate a negative/leftward run of –7 and yield the same negative slope. 2 4 6 8 2 10 12 14

15. Determine the rate of change.12 10 7 8 6 4
The run between the green points is 7. The line does not rise between the green points, so rise =0.
No matter what two points are chosen on the red line, rise will be 0 and run will be positive (rightward) or negative (leftward). Since 0/+=0 and 0/-=0, the slope will 0. 2
Horizontal lines have a slope of zero. 2 4 6 8 10 12 14

16. Determine the rate of change.12 6 10 8
(undefined) 6 4
Vertical lines have slopes which are undefined.
The rise between the green points is 6, but, this time, the run is 0. 2 2 4 6 8 10 12 14

17. Summary: Types of Rates of Change
Summary: Types of Slopes
positive
negative
undefined
zero

18. = 8 Determine the rate of change of this line.
Which points will you use to determine rise and run? 40 5
M=rise/run
To measure rise and run, we could count squares between 2 points on the line. From the graph it is easy to read the coordinates of (2,30) and (7,70) since these fall on grid lines.
Mark these 2 points and use the given scales to measure rise and run.
Rise =40
Run=5
M=40/5
M=8
= 8

19. Determine the rate of change of the line segment.–2 60

20. Draw a line which has a rate of change of
Draw a line which has a slope of 2

21. Draw a line which has a rate of change of–5 6 –5 6

22. Draw a line which has a rate of change of …
b) 3 1 –3 3 1 1 –3 3 1