Find the difference quotient of $LaTeX: \displaystyle f(x)=5 x - 1$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=5 h + 5 x - 1$ and expanding gives $LaTeX: \displaystyle f(x+h)=5 h + 5 x - 1$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(5 h + 5 x - 1)-(5 x - 1)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{5 h}{h}=5$