Question

The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution?

(0, 2)
(2, 0)
(1, −2)
(−2, 1)

Answer 1

You need to check which ordered paid is in the shaded region. Since the line is dashed a point on the line is NOT a solution​.
(2,0) is the only one in the shaded region

Answer 2

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)`