Which direction should be shaded for the inequality (using the boundary line )?
- Shade to the right of the line
- Shade to the left of the line
- Shade above the line
- Shade below the line (correct answer)
Explanation: This question tests your understanding of graphing linear inequalities and how the solution is represented as a shaded half-plane on the coordinate plane. To graph a linear inequality like y > 2x + 1, we first graph the boundary line y = 2x + 1 (replacing the inequality with equals). Then we decide: is it a solid line (if the inequality includes 'or equal to,' like ≥ or ≤) or a dashed line (if it's strict, like > or <)? Finally, we shade the half-plane that makes the inequality true—above the line for y > or y ≥, below for y < or y ≤. For y < 3x + 2, graph the boundary y = 3x + 2 (dashed since < is strict), then test (0,0): 0 < 2 is true, so shade the side with (0,0), which is below the line. Choice B correctly identifies shading below the line because y < requires lower y-values than the boundary. If you chose A, that's a common mix-up—gently note that < means below, while > means above; practice with test points to confirm. For shading direction with y inequalities: y > [line] means 'y is greater than the line' = shade above (higher y-values). y < [line] means 'y is less than the line' = shade below (lower y-values). Or use the test point method: pick (0, 0) if it's not on the line, substitute into the inequality, and if true, shade the side with (0, 0); if false, shade the other side!