[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}\\\\
-------------------------------\\\\
\stackrel{f(x)}{y}=2x+2 \qquad
\begin{cases}
x_1=-3\\
x_2=4
\end{cases}\implies \cfrac{f(4)-f(-3)}{4-(-3)}\implies \cfrac{f(4)-f(-3)}{4+3}
\\\\\\
\cfrac{[2(4)+2]~~-~~[2(-3)+2]}{7}\implies \cfrac{10-(-4)}{7}\implies \cfrac{10+4}{7}\implies \cfrac{2}{1}[/tex]
