to the risk of being redundant
[tex]\bf slope = m = \cfrac{rise}{run} \implies
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
f(x)= \sqrt{x} \qquad
\begin{cases}
x_1=4\\
x_2=9
\end{cases}\implies \cfrac{f(9)-f(4)}{9-4}\implies \cfrac{\sqrt{9}-\sqrt{4}}{5}
\\\\\\
\cfrac{3-2}{5}\implies \cfrac{1}{5}[/tex]
