Question

Can somebody explain this to

Answer 1

Check the picture below.

$slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(x_2)-f(x_1)}{2-0}\implies \cfrac{0~~ - ~~1}{2}\implies -\cfrac{1}{2}$