Chapter 9.3, Problem 4GP

To determine

To calculate: The constant rate of change for the given linear function. Also, interpret its meaning.

Answer to Problem 4GP

The constant rate of change is $\$2\text{ per pound}$ .

Explanation of Solution

Given information:

The following graph:

Calculation:

Choose any two points from the line such as $\text{(1,2)}$ and $\text{(2,4)}$ .

The number of Poundschanges from $1$ to $2$ and the total sales from $2$ to $4$ .

Find the unit rate to determine the constant rate of change.

  $\begin{array}{l}\text{ Rate of change = }\frac{\text{Change in total sales}}{\text{Change in number of pounds}}\\ =\frac{\$(4-2)}{(2-1)\text{ Pounds}}[\text{Substitute]}\\ =\frac{\$2}{\text{1 Pound}}[\text{Simplify]}\\ \end{array}$

The total sales is increasing by $\$2$ for every Pound.