Graphing Inequalities in Two Variables

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What is a linear inequality in two variables?

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What does it mean if a point lies on the boundary line of a linear inequality?

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If a point lies on the boundary line of a linear inequality, it is not considered a solution if the inequality is strict (e.g., < or >). If the inequality is non-strict (e.g., \leq or \geq), then the point is considered a solution.

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How do you determine if a point is a solution to a linear inequality?

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

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What is the significance of a dotted line in graphing inequalities?

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A dotted line indicates that the points on the line are not included in the solution set of the inequality. This is used for strict inequalities (e.g., < or >).

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What does a solid line represent in graphing inequalities?

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A solid line indicates that the points on the line are included in the solution set of the inequality. This is used for non-strict inequalities (e.g., \leq or \geq).

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What does the shaded region in a graph of a linear inequality represent?

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The shaded region in a graph of a linear inequality represents all the possible solutions to the inequality.

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How can you tell which side of the line to shade when graphing an inequality?

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To determine which side of the line to shade, you can test a point not on the line (commonly (0,0)). Substitute the coordinates of the point into the inequality. If the inequality is true, shade the side containing that point.

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What is the solution set of an inequality?

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The solution set of an inequality is the set of all points (x, y) that satisfy the inequality.