[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}\\\\
-------------------------------[/tex]
[tex]\bf f(x)=20\left( \frac{1}{4} \right)^x \qquad
\begin{cases}
x_1=1\\
x_2=2
\end{cases}\implies \cfrac{f(2)-f(1)}{2-1}
\\\\\\
\cfrac{20\left( \frac{1}{4} \right)^2~~-~~20\left( \frac{1}{4} \right)^1}{1}\implies
\cfrac{20\cdot \frac{1^2}{4^2}~~-~~20\cdot \frac{1^1}{4^1}}{1}
\\\\\\
\cfrac{\frac{20}{16}-\frac{20}{4}}{1}\implies \cfrac{\frac{5}{4}-5}{1}\implies \cfrac{\frac{5-20}{4}}{1}\implies \cfrac{-\frac{15}{4}}{1}\implies -\cfrac{15}{4}\implies -3\frac{3}{4}[/tex]
