Check all points for being the solutions of inequality [tex] y<0.5x+2 [/tex]:
1. For point (–3, –2) you have that x=-3 and y=-2, then
[tex] -2<0.5\cdot (-3)+2=-1.5+2=0.5 [/tex] - true.
2. For point (–2, 1) you have that x=-2 and y=1, then
[tex] 1\le 0.5\cdot (-2)+2=-1+2=1 [/tex] - false.
3. For point (–1, –2) you have that x=-1 and y=-2, then
[tex] -2<0.5\cdot (-1)+2=-0.5+2=1.5 [/tex] - true.
4. For point (–1, 2) you have that x=-1 and y=2, then
[tex] 2>0.5\cdot (-1)+2=-0.5+2=1.5 [/tex] - false.
5. For point (1, –2) you have that x=1 and y=-2, then
[tex] -2<0.5\cdot 1+2=0.5+2=2.5 [/tex] - true.
6. For point (1, 2) you have that x=1 and y=2, then
[tex] 2<0.5\cdot 1+2=0.5+2=2.5 [/tex] - true.
Answer: points (–3, –2), (–1, –2), (1, –2), (1, 2) apply.
