What best describes the rate of change?

• A. A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.
• B. A ratio that compares the total change in both variables without regard to type.
• C. A ratio of the independent variable to the dependent variable.
• D. The sum of the changes in the dependent variable and the independent variable.

Answer: (A)

The rate of change shows how much the dependent variable changes for every unit change in the independent variable. It’s expressed as a ratio of the amount the dependent variable changes to the amount the independent variable changes. For example, if y increases from 4 to 10 as x increases from 1 to 3, the rate of change is (10−4)/(3−1) = 6/2 = 3, meaning y changes by 3 for each 1 unit increase in x. This captures the idea that the rate of change compares how much y changes relative to how much x changes. It’s not about total changes added together, nor a ratio of the independent to the dependent variable, nor a sum of changes.