Find the difference quotient of $LaTeX: \displaystyle f(x)=10 x - 4$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=10 h + 10 x - 4$ and expanding gives $LaTeX: \displaystyle f(x+h)=10 h + 10 x - 4$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(10 h + 10 x - 4)-(10 x - 4)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{10 h}{h}=10$