we have
\(y> -3x+2\)
The solution is the shaded area above the dotted line
we know that
If a point is a solution of the inequality, then the coordinates of the point must satisfy the inequality
We will verify all cases to determine the solution of the problem
Case A) Point \((0,2)\)
\(x=0\\y=2\)
Substitute the value of x and y in the inequality and verify
\(2> -3*0+2\)
\(2>2\) -------> is not true
therefore
the point \((0,2)\) is not a solution of the inequality
Case B) Point \((2,0)\)
\(x=2\\y=0\)
Substitute the value of x and y in the inequality and verify
\(0> -3*2+2\)
\(0>-4\) -------> is true
therefore
the point \((2,0)\) is a solution of the inequality
Case C) Point \((1,-2)\)
\(x=1\\y=-2\)
Substitute the value of x and y in the inequality and verify
\(-2> -3*1+2\)
\(-2>-1\) -------> is not true
therefore
the point \((1,-2)\) is not a solution of the inequality
Case D) Point \((-2,1)\)
\(x=-2\\y=1\)
Substitute the value of x and y in the inequality and verify
\(1> -3*(-2)+2\)
\(1>8\) -------> is not true
therefore
the point \((-2,1)\) is not a solution of the inequality
therefore
the answer is the Point B
\((2,0)\)
To better understand the problem see the attached figure
