College Algebra, Chapter 3, 3.4, Section 3.4, Problem 10

A function $\displaystyle g(x) = 5 + \frac{1}{2} x$. Determine the average rate of change of the function between $x = 1$ and $x = 5$.


$\begin{equation} \begin{aligned} \text{average rate of change } =& \frac{g(b) - g(a)}{b - a} && \text{Model} \\ \\ \text{average rate of change } =& \frac{g(5) - g(1)}{5 - 1} && \text{Substitute } a = 1 \text{ and } b = 5 \\ \\ \text{average rate of change } =& \frac{\displaystyle 5 + \frac{1}{2} (5) - \left[ 5 + \frac{1}{2} (1) \right] }{4} && \text{Simplify} \\ \\ \text{average rate of change } =& \frac{\displaystyle 5 + \frac{5}{2} - 5 - \frac{1}{2} }{4} && \text{Combine like terms} \\ \\ \text{average rate of change } =& \frac{\displaystyle \frac{4}{2}}{4} && \text{Simplify} \\ \\ \text{average rate of change } =& \frac{2}{4} && \text{Reduce to lowest term} \\ \\ \text{average rate of change } =& \frac{1}{2} && \text{Answer} \end{aligned} \end{equation}$