[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)=-2x+1 \qquad
\begin{cases}
x_1=-5\\
x_2=1
\end{cases}\implies \cfrac{f(1)-f(-5)}{-5-1}
\\\\\\
\cfrac{[-2(1)+1]~~-~~[-2(-5)+1]}{-6}\implies \cfrac{[-1]~~-~~[11]}{-6}
\\\\\\
\cfrac{-12}{-6}\implies 2[/tex]
