What is Average rate of change?

Let $f$ be defined on an interval $I$, and $a \neq b$ in $I$. The average rate of change of $f$ between $a$ and $b$ is

It is the slope of the secant line through the points $\bigl(a, f(a)\bigr)$ and $\bigl(b, f(b)\bigr)$ of the curve.