Find the difference quotient of $LaTeX: \displaystyle f(x)=- 5 x - 2$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 5 h - 5 x - 2$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 5 h - 5 x - 2$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 5 h - 5 x - 2)-(- 5 x - 2)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 5 h}{h}=-5$