Find the difference quotient of $LaTeX: \displaystyle f(x)=10 x + 8$ .

The difference quotient is $LaTeX: \displaystyle \frac{f(x+h)-f(x)}{h}$ . Evaluating $LaTeX: \displaystyle f(x+h)=10 h + 10 x + 8$ and expanding gives $LaTeX: \displaystyle f(x+h)=10 h + 10 x + 8$ Evaluating the difference quotient gives $LaTeX: \displaystyle \frac{(10 h + 10 x + 8)-(10 x + 8)}{h}$ Simplifying gives $LaTeX: \displaystyle \frac{10 h}{h}=10$