What Is the Formula for the Average Rate of Change?

Average rate of change refers to the degree to which a quantity increases or decreases in comparison to changes in another quantity. The generic rate of change formula divides the change in the quantity of interest by the change of the comparison quantity.

The slope of a line on a graph is an example of rate of change. The change in y, divided by the change in x, represents the average rate of change. If the function presented on a graph is not linear, the average rate of change is the same as the slope of a straight line drawn from the start to the end points of the line segment. For example, the average rate of change from the point (0,0) to (100, 100) is the same as the slope of a line that goes through points (0,0) and (100,100), even if the function is nonlinear between those two points.

Another example of an average rate of change is gallons of gasoline used per hour while driving. The exact rate at which gasoline is consumed varies while driving, depending on how much the driver is pressing the acceleration pedal. When going down a hill, the car uses less gas because gravity pulls the car down the hill. On the other hand, when the car goes up a hill, it requires more gas. The average rate of gas used per hour depends on the start and end points of interest and ignores the details of the trip between the two endpoints. If a car has 10 gallons of gas at the start of a 2-hour trip and 6 gallons of gas at the end of the trip, the average gasoline consumption is obtained by dividing 4 gallons by 2 hours. The calculation yields 2 gallons of gas per hour.