1. Rate of Change a.k.a. Slope

2. Rate of Change of a Linear Relationship
rise
run
Rate of Change =
The rate of change (slope) of a linear relationship is the steepness of the line.

3. Rates of change are seen everywhere.

4. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

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

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

7. They often represent the rate of change as a percentage.

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

9. The steepness of wheelchair ramps is of great importance for safety.1 12
Rate of change of wheelchair ramp =
If the rise is 1.5 m, what is the run?
Answer: 18 m because

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

11. Determine the rate of change of each staircase.2 3

12. Determine the slope (rate of change) of the line segment.
5 cm
9 cm
We use the letter m because in French the word for “to go up” is monter.
René Descartes ( ) was from France and he was the first to define the Cartesian Plane.

13. Determine the slope of the line segment.y 6 4 x

14. Determine the slope of the line segment.y –5 7 x

15. Determine the slope of the line segment.y 6
Horizontal lines have a slope of zero. x

16. Determine the slope of the line segment.y 5
Vertical lines have slopes which are undefined. x

17. positive
negative
undefined
zero

18. Determine the rate of change.
Which points will you use to determine rise and run?
Earnings 4 20
= $5/hr
What does this rate of change represent?
Number of Hours Worked
The hourly wage