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

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