Chapter 3, Problem 27SGR

To determine

To find: Rate of change.

Answer to Problem 27SGR

Rate of change of given graph is $m=3$

Explanation of Solution

Given equation:

Points on the graph are

  $\begin{array}{l}\left(x_1,y_1\right)=\left(1,3\right)\\ \left(x_2,y_2\right)=\left(-2,-6\right)\end{array}$

Concept:

When two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given

Rate of change = Slope = $m=\frac{y_2-y_1}{x_2-x_1}$

Given points are

  $\begin{array}{l}\left(x_1,y_1\right)=\left(1,3\right)\\ \left(x_2,y_2\right)=\left(-2,-6\right)\end{array}$

Rate of change = $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}\Rightarrow m=\frac{-6-3}{-2-1}\\ \Rightarrow m=\frac{-9}{-3}\\ \Rightarrow m=3\end{array}$

Therefore

Rate of change of given graph is $m=3$