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

we know that

If a point qualifies as a solution for the inequality

then

That point must fulfill the inequality

we have

The solution to the inequality is the shaded region below the solid red line

refer to the attached figure for greater understanding of the task

Step 1

Point

Substitute the values of x and y into the inequality

-------> is false

consequently

Point A does not satisfy the inequality

Refer to the attached figure------> point A lies outside the shaded area

Step 2

Point

Substitute the values of x and y into the inequality

-------> is true

thus

Point B qualifies as a solution for the inequality

Refer to the attached figure------> point B resides within the shaded area

Step 3

Point

Substitute the values of x and y into the inequality

-------> is false

therefore

Point C does not qualify as a solution for the inequality

Refer to the attached figure------> point C does not lie within the shaded area

Step 4

Point

Substitute the values of x and y into the inequality

-------> is false

therefore

Point D does not qualify as a solution for the inequality

Refer to the attached figure------> point D is not found within the shaded area

the answer is