Question

I'm stuck on this problem I need help in identifying which shaded region is the solution

Answer 1

Explanation:

We have the following system of inequalities

`\begin{gathered} y>\: -3x-4 \\ y\ge3x-2 \end{gathered}`

We determine two points for each inequality, to be able to draw the line, just like this:

`\begin{gathered} y(-2)=-3(-2)-4=6-4=2\rightarrow(-2,2) \\ y(0)=-3(0)-4=0-4=-4\rightarrow(0,-4) \\ \\ y(-1)=3(-1)-2=-3-2=-5\rightarrow(-1,-5) \\ y(0)=3(0)-2=0-2=-2\rightarrow(0,-2) \end{gathered}`

We locate the points and then draw the lines.

Then, since they are inequalities, what we do is shade according to the sign they have.

In this case and are all the values above the line, and in the first equations the line is dotted because it does not include the line, finally the graph would be: