Find the difference quotient of $LaTeX: \displaystyle f(x)=2 x - 6$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=2 h + 2 x - 6$ and expanding gives $LaTeX: \displaystyle f(x+h)=2 h + 2 x - 6$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(2 h + 2 x - 6)-(2 x - 6)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{2 h}{h}=2$