Chapter 3.3, Problem 17PPS

To determine

The rate of change represented in the given graph.

Answer to Problem 17PPS

  $\frac{1}{2}$

Explanation of Solution

Given information:

The graph:

  

Concept Used:

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

In order to find the rate of change of the line represented in the graph, observe that the line passes through the points $\left(x_1,y_1\right)=\left(-4,-6\right),\text{ and }\left(x_2,y_2\right)=\left(4,-2\right)$ . So, using the slope of line passing through two points formula, it gives

  $\begin{array}{c}\text{Rate of change}=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-2-\left(-6\right)}{4-\left(-4\right)}\\ =\frac{-2+6}{4+4}\\ =\frac{4}{8}\\ =\frac{1}{2}\end{array}$

Thus, the rate of change of the given graph is $\frac{1}{2}$ .