Linear Inequalities

Concept:The inequality $-x + 2y < 0$ represents all points below the dashed line $y = \frac{x}{2}$.Explanation:Rewrite the inequality: $-x + 2y < 0 \implies 2y < x \implies y < \frac{x}{2}$.The boundary line is $y = \frac{x}{2}$, which passes through the origin with slope $\frac{1}{2}$.Because the inequality is strict ($<$), the boundary line is dashed (not solid).The region $y < \frac{x}{2}$ is the area below that line.Among the given graph options, the one with a dashed line through (0,0) with slope $\frac{1}{2}$ and shading below it correctly represents the inequality.Based on typical textbook representation, this matches option A.Answer: