Question

I need help with this question to get the right answer

Answer 1

The blue region consists on the intersection of two regions. The region above the decreasing line, and the region below the increasing line. Those lines are

$\begin{cases}y=x+8 \\ y=-\frac{1}{2}x\end{cases}$

Those are the boundaries of those regions. Since both lines are dashed lines, the regions do not include those lines. The increasing line is the one with the positive slope

$y=x+8$

Since our region is below this line, the y values must be less than the values on this line, and the inequality that represents this region is

$yThe decreasing line is the one with the negative slope[tex]y=-\frac{1}{2}x$

Since our region is above this line, the y values must be greater than the values on this line, and the inequality that represents this region is

$y>-\frac{1}{2}x$

Combining those two regions, we have their intersection which is the desired blue region

$y-\frac{1}{2}x$