Find the difference quotient of $LaTeX: \displaystyle f(x)=8 - 5 x$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 5 h - 5 x + 8$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 5 h - 5 x + 8$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 5 h - 5 x + 8)-(8 - 5 x)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 5 h}{h}=-5$