Rate of Change

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then

rateofchange= changeiny changeinx

Rates of change can be positive or negative. This corresponds to an increase or decrease in the y -value between the two data points. When a quantity does not change over time, it is called zero rate of change.

Positive rate of change

When the value of x increases, the value of y increases and the graph slants upward.

Negative rate of change

When the value of x increases, the value of y decreases and the graph slants downward.

Zero rate of change

When the value of x increases, the value of y remains constant. That is, there is no change in y value and the graph is a horizontal line.

Example:

Use the table to find the rate of change. Then graph it.

TimeDriving(h) x DistanceTravelled(mi) y 2 80 4 160 6 240

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

rateofchange= changeiny changeinx = changeindistance changeintime = 16080 42 = 80 2 = 40 1

The rate of change is 40 1 or 40 . This means a vehicle is traveling at a rate of 40 miles per hour.