Chapter 9.3, Problem 3GP

To determine

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

Answer to Problem 3GP

The constant rate of change is $\text{0}\text{.5 inches per week}$ .

Explanation of Solution

Given information:

The following graph:

Calculation:

Choose any two points from the line such as $\text{(0,3)}$ and $\text{(2,4)}$ .

The number of weeks changes from $\text{0}$ to $2$ and height of the plant changes from $3$ to $4$ .

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

  $\begin{array}{l}\text{ Rate of change = }\frac{\text{Change in height}}{\text{Change in time}}\\ =\frac{(4-3)\text{ in}\text{.}}{(2-0)\text{ weeks}}[\text{Substitute]}\\ =\frac{\text{1 in}\text{.}}{\text{2 weeks}}[\text{Simplify]}\\ =\frac{\text{0}\text{.5 in}\text{.}}{1\text{ week}}[\text{Write as unit rate]}\\ \end{array}$

The plant is growing by a height of $\text{0}\text{.5 inches}$ every week.