[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)=2^x-1 \qquad
\begin{cases}
x_1=0\\
x_2=3
\end{cases}\implies \cfrac{f(3)-f(0)}{3-0}
\\\\\\
\cfrac{[2^3-1]~~-~~[2^0-1]}{3}\implies \cfrac{[8-1]~~-~~[1-1]}{3}
\\\\\\
\cfrac{7-0}{3}\implies \cfrac{7}{3}[/tex]
