Find the difference quotient of $LaTeX: \displaystyle f(x)=9 x + 7$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=9 h + 9 x + 7$ and expanding gives $LaTeX: \displaystyle f(x+h)=9 h + 9 x + 7$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(9 h + 9 x + 7)-(9 x + 7)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{9 h}{h}=9$