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

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