Chapter 5.6, Problem 44E

To determine

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

Answer to Problem 44E

  $y\le 2x+1$

Explanation of Solution

Given information: The points (2, 5) and (-3,-5) lie on boundary line of an inequality. The points (6, 5) and (-2,-3) are the solutions of the inequality.

The line passing through the points (2,5) and (-3,-5) is given by

  $\begin{array}{l}\frac{y-5}{x-2}=\frac{-5-5}{-3-2}\\ \Rightarrow \frac{y-5}{x-2}=\frac{-10}{-5}\\ \Rightarrow \frac{y-5}{x-2}=2\\ \Rightarrow y-5=2(x-2)\\ \Rightarrow y-5=2x-4\\ \Rightarrow y=2x+1\end{array}$

This is the boundary line of required inequality.

Now, the point (6, 5) is a solution of required inequality. Putting this value in the line $y=2x+1$ we get

  $\begin{array}{l}6=2(5)+1\\ \Rightarrow 6=10+1\\ \Rightarrow 6=11\end{array}$

This is possible only when if we put $\le$ in place of =

Hence the required inequality is $y\le 2x+1$ and its graph is as follows-

  

The shaded region is the graph of required inequality.