Graph linear inequalities and systems of linear inequalities as half-plane solution regions.
Choose solid or dashed boundary for an inequality
Problem
For \(y~\le~3x~+~1\), determine the boundary style, whether equality is included, and whether the inequality is inclusive or strict.
Big Picture
What this problem is really about
Boundary style comes entirely from whether equality is allowed. We’ll replace the inequality sign with equality to identify the boundary, inspect the original symbol for an equality bar, and map that inclusion decision to solid or dashed styling. This strict-versus-inclusive classification is separate from which side of the line would be shaded.
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