Find the difference quotient of $LaTeX: \displaystyle f(x)=- 6 x - 8$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=- 6 h - 6 x - 8$ and expanding gives $LaTeX: \displaystyle f(x+h)=- 6 h - 6 x - 8$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(- 6 h - 6 x - 8)-(- 6 x - 8)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{- 6 h}{h}=-6$