Find the difference quotient of $LaTeX: \displaystyle f(x)=9 x - 1$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=9 h + 9 x - 1$ and expanding gives $LaTeX: \displaystyle f(x+h)=9 h + 9 x - 1$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(9 h + 9 x - 1)-(9 x - 1)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{9 h}{h}=9$