Chapter 5.6, Problem 45E

To determine

To write: an inequality from given information and graph it.

Answer to Problem 45E

  $y\le 3x+5$

Explanation of Solution

Given information: The points (-7, -16) and (1, 8) lie on boundary line of an inequality. The points (-7, 0) and (3, 14) are not the solutions of the inequality.

The line passing through the points (-7, -16) and (1, 8) is given by

  $\begin{array}{l}\frac{y-8}{x-1}=\frac{-16-8}{-7-1}\\ \Rightarrow \frac{y-8}{x-1}=\frac{-24}{-8}\\ \Rightarrow \frac{y-8}{x-1}=3\\ \Rightarrow y-8=3(x-1)\\ \Rightarrow y-8=3x-3\\ \Rightarrow y=3x+5\end{array}$

This is the boundary line of required inequality.

Now, the point (-7, 0) is not a solution of required inequality. Putting this value in the line $y=3x+5$ we get

  $\begin{array}{l}0=3(-7)+5\\ \Rightarrow 0=-21+5\\ \Rightarrow 0=-16\end{array}$

This is not possible if we put $\le$ in place of =

Hence the required inequality is $y\le 3x+5$ and its graph is as follows-

  

The shaded region is the graph of required inequality.