Question

The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?

A.( 2, 3)

B.

(3, –2)

C. (2, 1)

D. (–1, 3)

Answer 1

just a matter of subbing answer choices into ur inequality to see which is true.
answer is : (3,-2)

Answer 2

we know that

If a point is a solution of the inequality

then

The point must satisfy the inequality

we have

`y\leq -x+1`

The solution of the inequality is the shaded area below the solid red line

see the attached figure to better understand the problem

Step 1

Point
`A(2,3)`

Substitute the value of x and the value of y in the inequality

`x=2\ y=3`

`3\leq -2+1`

`3\leq -1` -------> 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(3,-2)`

Substitute the value of x and the value of y in the inequality

`x=3\ y=-2`

`-2\leq -3+1`

`-2\leq -2` -------> 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(2,1)`

Substitute the value of x and the value of y in the inequality

`x=2\ y=1`

`1\leq -2+1`

`1\leq -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(-1,3)`

Substitute the value of x and the value of y in the inequality

`x=-1\ y=3`

`3\leq 1+1`

`3\leq 2` -------> 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(3,-2)`