[tex]\bf slope = \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{f(x_2)-f(x_1)}{x_2-x_1}\impliedby
\begin{array}{llll}
\textit{average rate}\\
\textit{of change}
\end{array}
\\\\\\
f(x)=2^{x}+1\quad
\begin{cases}
x_1=0\\
x_2=2
\end{cases}\implies \cfrac{f(x_2)-f(x_1)}{x_2-x_1}\implies \cfrac{(2^{2}+1)-(2^{0}+1)}{2-0}[/tex]
just to point out, you didn't include the graph, in this case, it doesn't matter much, that's not the case most times... just so you know
