Find the difference quotient of $LaTeX: \displaystyle f(x)=5 x - 10$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=5 h + 5 x - 10$ and expanding gives $LaTeX: \displaystyle f(x+h)=5 h + 5 x - 10$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(5 h + 5 x - 10)-(5 x - 10)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{5 h}{h}=5$