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

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