Which inequality represents the half-plane above the line y = −2?

Correct answer: y > −2

The boundary y = −2 is a horizontal line. Every point on it has y-coordinate equal to −2, while points above it have y-coordinates greater than −2. Therefore the required half-plane is y > −2, so option C is correct. The inequality is strict because “above the line” excludes the boundary itself; if the boundary were included, the expression would be y ≥ −2. Option B, y < −2, represents the region below the line. Options A and D concern the vertical boundary x = −2, describing regions to its right and left respectively, so they cannot represent a region above y = −2. The key distinction is that vertical position is determined by the y-coordinate, not by x.