Graphing: Rates of Change (Math 8)

What is a ratio? A ratio is the comparison of two numbers and in math is typically written in fraction form.

First, what is a rate? A rate is a special ratio. A rate compares two numbers with different units of measures, such as distance (miles) and time (hours).

So, what is a rate of change? A rate of change is how one quantity changes in relation to another quantity. In math we look at how the output values change in relationship to the input values.

Typically, you will ask yourself,

“As the input values are increasing, what is going on with the output values?”.

Positive Rates of Change

Negative Rates of Change

Zero Rate of Change

The following graphs (or functional relationships) are all going to represent you riding your bike. Each graph will start the bike ride at your home. The input values will represent the time (in hours) you are biking and the output values will represent the distance (in miles) you are from home while biking.