Graphing Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

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What does a dashed boundary line indicate in graphing linear inequalities?

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A dashed boundary line indicates that the points on the line are not included in the solution set, which occurs when the inequality does not have an 'or equal to' component.

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What does a solid boundary line indicate in graphing linear inequalities?

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A solid boundary line indicates that the points on the line are included in the solution set, which occurs when the inequality has an 'or equal to' component.

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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, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is part of the solution set.

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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 inequality symbol in graphing?

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The inequality symbol determines whether the boundary line is dashed or solid and indicates which side of the line is included in the solution set.

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What is the first step in solving a linear inequality?

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The first step is to isolate the variable on one side of the inequality, similar to solving a linear equation.

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Substitute the point's coordinates into the inequality. If the resulting statement is true, the point is part of the solution set.