Find the difference quotient of $LaTeX: \displaystyle f(x)=10 - 3 x$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 3 h - 3 x + 10$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 3 h - 3 x + 10$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 3 h - 3 x + 10)-(10 - 3 x)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 3 h}{h}=-3$