Linear Inequalities

Concept:The graph of a linear inequality $x+y<6$ is the half-plane below the dashed boundary line $x+y=6$, including the origin.Explanation:The boundary line is $x+y=6$.Find intercepts: $(6,0)$ and $(0,6)$.Because the inequality is strict ($<$), the line is dashed.Test the origin $(0,0)$: $0+0 < 6$ is true, so the region containing the origin is shaded.Thus, the correct graph shows a dashed line through $(6,0)$ and $(0,6)$ with shading below the line (toward the origin).Answer: