[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^2-7x \qquad
\begin{cases}
x_1=2\\
x_2=5
\end{cases}\implies \cfrac{f(5)-f(2)}{5-2}
\\\\\\
\cfrac{[2(5)^2-7(5)]~~-~~[2(2)^2-7(2)]}{3}\implies \cfrac{[50-35]~~-~~[8-14]}{3}
\\\\\\
\cfrac{15-[-6]}{3}\implies \cfrac{15+6}{3}\implies \cfrac{21}{3}\implies 7 [/tex]
