[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)= x^2-3x-4\qquad \begin{cases} x_1=-1\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(-1)}{3-(-1)} \\\\\\ \cfrac{[(3)^2-3(3)-4]~~-~~[(-1)^2-3(-1)-4]}{3+1} \\\\\\ \cfrac{[-4]~~-~~[1+3-4]}{4}\implies \cfrac{[-4]-[0]}{4}\implies -1[/tex]
