Question

The solutions to the inequality y < to -x+1 sre shaded on the graph. Which point is a solution

Answer 1

Answer:  B.  (3,-2)

There are two ways to confirm this is the answer. The first is to note that (3,-2) is on the boundary, so it is part of the solution set. This only works if the boundary line is a solid line (as opposed to a dashed or dotted line).

The second way is to plug (x,y) = (3,-2) into the given inequality to find that

$y \le -x+1\\\\-2 \le -3+1\\\\-2 \le -2$

which is a true statement. So this confirms that (3,-2) is in the solution set of the inequality.