Find the difference quotient of $LaTeX: \displaystyle f(x)=- 7 x - 8$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 7 h - 7 x - 8$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 7 h - 7 x - 8$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 7 h - 7 x - 8)-(- 7 x - 8)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 7 h}{h}=-7$