we know that
If a point is a solution of the inequality
then
The point must satisfy the inequality
we have
\(y>-3x+2\)
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 \(A(0,2)\)
Substitute the value of x and the value of y in the inequality
\(x=0\ y=2\)
\(y>-3x+2\)
\(2>-3*0+2\)
\(2>2\) -------> 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 \(B(2,0)\)
Substitute the value of x and the value of y in the inequality
\(x=2\ y=0\)
\(y>-3x+2\)
\(0>-3*2+2\)
\(0>-4\) -------> 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 \(C(1,-2)\)
Substitute the value of x and the value of y in the inequality
\(x=1\ y=-2\)
\(y>-3x+2\)
\(-2>-3*1+2\)
\(-2>-1\) -------> 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 \(D(-2,1)\)
Substitute the value of x and the value of y in the inequality
\(x=-2\ y=1\)
\(y>-3x+2\)
\(1 >-3*-2+2\)
\(1 >8\) -------> 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
\(B(2,0)\)
