Find the difference quotient of $LaTeX: \displaystyle f(x)=4 - 9 x$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 9 h - 9 x + 4$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 9 h - 9 x + 4$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 9 h - 9 x + 4)-(4 - 9 x)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 9 h}{h}=-9$