Question

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

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

$B(3,-2)$