[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}\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\stackrel{y}{f(x)}= x^2+2 \qquad
\begin{cases}
x_1=1\\
x_2=2
\end{cases}\implies \cfrac{f(2)-f(1)}{2-1}\implies \cfrac{(2^2+2)-(1^2+2)}{1}
\\\\\\
\cfrac{6-3}{1}\implies 3 [/tex]
