Find the difference quotient of $LaTeX: \displaystyle f(x)=- 8 x - 2$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 8 h - 8 x - 2$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 8 h - 8 x - 2$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 8 h - 8 x - 2)-(- 8 x - 2)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 8 h}{h}=-8$