Chapter 1.3, Problem 67HP

To determine

To find: the inequality represented by the graph.

Answer to Problem 67HP

Option D represented the graph.

Explanation of Solution

Given information:

Given graph

  

And

 A. $y<\frac{2}{3}x+4$

 B. $y>\frac{2}{3}x+4$

 C. $y<\frac{3}{2}x+4$

 D. $y>\frac{3}{2}x+4$

 D. $y>\frac{3}{2}x+4$

Calculation:

First of all , we can immediately conclude that $A$ and $C$ are not our answer, because point $\left(0,0\right)$ lies in their shade. It leaves us with $B$ and $D$ option. Now we need to pick a point which is in shaded part let’s say $\left(-3,0\right)$ and try it with $B$ and $D$ inequalities.

Calculating For $B$ :

  $\begin{array}{l}0>\frac{2}{3}\cdot \left(-3\right)+4\\ 0>\frac{2}{\cancel{3}}\cdot \left(-\cancel{3}\right)+4\\ 0>-2+4\\ 0>2\end{array}$

Now for $D:$

  $\begin{array}{l}0>\frac{3}{2}\cdot \left(-3\right)+4\\ 0>\frac{-9}{2}+4\\ 0>-4.5+4\\ 0>-0.5\end{array}$

So, $D=y>\frac{3}{2}x+4$ is the solution.