Graph linear inequalities and systems of linear inequalities as half-plane solution regions.
Graph one linear inequality in slope-intercept form
Problem
For \(y\le~2x+1\), identify boundary equation, style, and shading direction.
Big Picture
What this problem is really about
A linear inequality graph combines a boundary decision with a half-plane decision. We’ll replace the inequality sign by equality to construct the line from its slope and intercept, use the presence or absence of equality to determine whether that boundary is included, and test a point off the line to identify the solution side. These checks separate line direction from shading direction.
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