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=-(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=-(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>-(1)/(2)x`

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

`y-(1)/(2)x`