Chapter 9.3, Problem 36STP

To determine

To calculate : the constant rate of change for the linear function in the graph.

Answer to Problem 36STP

The constantrate of changefor the line is $-0.5$ .

Explanation of Solution

Given information :

Consider the graph:

Formula used:

The slope or rate of change of a line:

  $m=\frac{y_2-y_1}{x_2-x_1}$ , where $x_2\ne x_1$

Calculation :

As per problem,

In a linear function, the slope, or rate of change, of the line is always constant.

Consider the points $(2,2)$ and $(5,0.5)$ on the line in the given graph.

Take $y_1=2,y_2=0.5,x_1=2,\text{ and }{x}_2=5$

So, the slope of the line:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\text{ [Write the formula]}\\ m=\frac{0.5-2}{5-2}\text{ [}{y}_1=2,y_2=0.5,x_1=2,x_2=5]\\ m=\frac{-1.5}{3}=-0.5\text{ [Simplify]}\end{array}$

Therefore, the constantrate of change, or slope, of the line is $-0.5$ .