[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}\\\\ f(x)= \cfrac{2x-1}{3x+5}\qquad \begin{cases} x_1=0\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(0)}{4-0}[/tex]
[tex]\bf \cfrac{~~\left( \frac{2(4)-1}{3(4)+5} \right)-\left( \frac{2(0)-1}{3(0)+5} \right)~~}{4}\implies \cfrac{~~\left( \frac{7}{17} \right)-\left( \frac{-1}{5} \right)~~}{4}\implies\cfrac{~~\left( \frac{7}{17} \right)+\left( \frac{1}{5} \right)~~}{4} \\\\\\ \cfrac{~~\frac{35+17}{85}~~}{4}\implies \cfrac{~~\frac{52}{85}~~}{\frac{4}{1}}\implies \cfrac{52}{85}\cdot \cfrac{1}{4}\implies \cfrac{13}{85}[/tex]
