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}
\\
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\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}
$