Procedure for Determining a Linear Inequality in Two Variables from its Graph
To determine the linear inequality represented by a given graph when the equation of its boundary line is known, apply a systematic procedure. First, identify the correct inequality symbol direction by selecting a test point from the shaded solution region. The origin is typically the easiest point to evaluate, provided it does not lie exactly on the boundary line. Substitute the test point's coordinates into the boundary line's expression to determine which inequality symbol ( or ) makes the resulting mathematical comparison true. Second, examine the style of the graphed boundary line to dictate if the inequality is strict or non-strict. If the boundary line is graphed as a solid line, points exactly on the line are included as solutions, meaning the equal sign must be grouped with the inequality symbol (forming or ). Conversely, if the boundary line is dashed, the line is excluded from the solution set, and the strict inequality symbol ( or ) must be used.
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Boundary Lines for Single-Variable Inequalities on the Coordinate Plane
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Procedure for Determining a Linear Inequality in Two Variables from its Graph
Graphing the Linear Inequality