Answer: Choice A
[tex]\begin{cases} y \le x+5 \\ y < -x+1\end{cases}[/tex]
Explanation:
The solid boundary line is the equation y = x+5. The idea is to pick two points on the line and then use them to find the slope. So let's use (-5,0) and (0,5). The slope is...
m = (y2-y1)/(x2-x1)
m = (5-0)/(0-(-5))
m = (5-0)/(0+5)
m = 5/5
m = 1
With the slope m = 1and the point (x1,y1) = (-5,0), we then use the point slope formula
y-y1 = m(x-x1)
y-0 = 1(x-(-5))
y = x+5
The same kind of steps will be used for the dashed line as well.
We see that the shaded region is below the solid boundary line y = x+5. So we will use a less than or equal sign here to indicate to shade below and have the boundary be solid.
The dashed line's equation is y = -x+1, and we also shade below it. So we use a less than sign. We don't use "or equal to" because the dashed line tells the reader "points on this dashed line do not count as solutions".
