What is the point (0,2) for the inequality y≤2x+1?

Correct answer: Not in the solution region

The governing concept is checking a point in a linear inequality by substitution. For the point (0,2), use x=0 and y=2 in y≤2x+1. The left side is 2, while the right side is 2(0)+1=1, so the inequality becomes 2≤1, which is false. Therefore the point is not in the solution region, making option C correct. It is also not on the boundary line, because the boundary equation y=2x+1 gives y=1 when x=0; the point on the boundary at x=0 would be (0,1), not (0,2). The symbol ≤ includes the boundary whenever equality holds, but equality does not hold here. Option A is rejected by the failed substitution, option B confuses the point with the boundary point, and option D is false because the origin is (0,0).