Lesson 5: Slope as a Rate of Change

Math 10C Module 4: Lesson 5

Module 4: General Relations

Lesson 5 Summary

In this lesson you investigated the following questions:

How is the slope of a line related to the dependent and independent variables of a graph?
How can slope be used to make predictions about the outcome of certain events?

You were previously introduced to slope as a way to measure the steepness of a line. In this lesson you learned how to draw a line with a given slope through a particular point. You also learned that, with a slope and a point, you can determine other points on the line. In this way, a slope can be used to predict other values on a line.

In the second half of Lesson 5 you investigated slope as a rate of change. Since the slope of a line is the vertical change divided by the horizontal, slope can also be interpreted as the change in the dependent variable compared to the change in the independent variable. You learned that you can interpret the slope in any context by writing the units of the slope as the units of the dependent variable divided by the units of the independent variable. For example, the slope of a distance-time graph could be metres per second, or a measure of speed.

In Module 5 you will investigate linear relations. You will build on your knowledge of slope by investigating the slopes of parallel and perpendicular lines. You will also see how the slope of a line is used to determine its equation.