Question

the solutions to the inequality y > −3x 2 are shaded on the graph. which point is a solution? a). (0, 2) b). (2, 0) c). (1, −2) d). (−2, 1)

Answer 1

(2,0)

All the other points listed are in the side of points that do not belong to the set of soluctions.

Answer 2

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