we know that
If a point is a solution of the inequality
then
The point must satisfy the inequality
we have
[tex]y>-3x+2[/tex]
The solution of the inequality is the shaded area above the dotted blue line
see the attached figure to better understand the problem
Step 1
Point [tex]A(0,2)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=0\ y=2[/tex]
[tex]y>-3x+2[/tex]
[tex]2>-3*0+2[/tex]
[tex]2>2[/tex] -------> is not true
therefore
The point A is not a solution for the inequality
See the attached figure------> the point A is not on the shaded area
Step 2
Point [tex]B(2,0)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=2\ y=0[/tex]
[tex]y>-3x+2[/tex]
[tex]0>-3*2+2[/tex]
[tex]0>-4[/tex] -------> is true
therefore
The point B is a solution for the inequality
See the attached figure------> the point B is on the shaded area
Step 3
Point [tex]C(1,-2)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=1\ y=-2[/tex]
[tex]y>-3x+2[/tex]
[tex]-2>-3*1+2[/tex]
[tex]-2>-1[/tex] -------> is not true
therefore
The point C is not a solution for the inequality
See the attached figure------> the point C is not on the shaded area
Step 4
Point [tex]D(-2,1)[/tex]
Substitute the value of x and the value of y in the inequality
[tex]x=-2\ y=1[/tex]
[tex]y>-3x+2[/tex]
[tex]1 >-3*-2+2[/tex]
[tex]1 >8[/tex] -------> is not true
therefore
The point D is not a solution for the inequality
See the attached figure------> the point D is not on the shaded area
the answer is
[tex]B(2,0)[/tex]
