The given inequalities are
[tex]y\leq-\frac{1}{2}x+3\text{ and }y>\frac{1}{2}x+1[/tex][tex]\text{Substitute x=2 in y=}-\frac{1}{2}x+3\text{ as follows.}[/tex]
[tex]y=-\frac{1}{2}(2)+3=-1+3=2[/tex]
The point is (2,2) lies in the given first inequality.
[tex]\text{Substitute x=2 in y=}\frac{1}{2}x+1\text{ as follows.}[/tex]
[tex]y=\frac{1}{2}(2)+1=1+1=2[/tex]
The point is (2,2) lies in the given second inequality.
Hence the point of intersection is (2,2).
Option D is the only graph that shows the point of intersection is (2,2).
