#5.6 Graphing Linear Inequalities in Two Variables

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What is a linear inequality in two variables?

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > (not including the line) and a solid line for ≤ or ≥ (including the line). Then shade the region that satisfies the inequality.

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What does it mean if a point is a solution to a linear inequality?

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A point is a solution to a linear inequality if it satisfies the inequality when the coordinates of the point are substituted into the inequality.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

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How can you determine if a point is a solution to an inequality?

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To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

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What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the coordinate plane.

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What is the significance of the boundary line in graphing inequalities?

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The boundary line separates the solution set from the non-solution set. Points on one side of the line satisfy the inequality, while points on the other side do not.

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