#### Answer

The average rate of change of a function between two points is the slope of the line between these two points.

#### Work Step by Step

The average rate of change of $f$ is given as
$\frac{\Delta y}{\Delta x}=\frac{f\left( {{x}_{2}} \right)-f\left( {{x}_{1}} \right)}{\left( {{x}_{2}}-{{x}_{1}} \right)}$
The mathematical symbol $\frac{\Delta y}{\Delta x}$ represents the change in y divided by the change in $x$.
The rate of change of the y coordinate of a function with respect to its x coordinate is the rate of change of the function.
The average rate of change of the function between two points is equal to the slope of the line between these two points.