The solutions to the inequality y< -x+1 are shaded on the graph. which point is a solution?

 
B) (3, –2)

Explanation: 
The inequality is y ≤ –x + 1
There are two ways to do this. You can try the four options by seeing where they lie on the graph, or by inputting them into the inequality and seeing if they check out. I am going to do a bit of both.

I know that the solution cannot have two positive coordinates because the first quadrant is not part of the solution, so I won't guess A or C. 
I'll try (3, –2) (which is option B).
On the graph, (3, –2) is on the line, which means it is part of the solution because the line is solid and the inequality is a greater than or equal to sign. 
Try it in the inequality: 
y ≤ –x + 1 
–2 ≤ –3 + 1 
–2 ≤ –2 yes this checks out.