Graphing Linear Inequalities in Two Variables

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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 the graph of a linear inequality represent?

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The graph of a linear inequality represents all the solutions to the inequality, which are the points that satisfy the inequality.

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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 a solution.

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What is the difference between a solid line and a dashed line in the graph of a linear inequality?

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

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What is the significance of the inequality symbol in a linear inequality?

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The inequality symbol indicates the relationship between the two expressions and determines which side of the line is included in the solution set.

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How can you express the solution set of a linear inequality?

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The solution set can be expressed in interval notation, set notation, or graphically on a coordinate plane.

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It indicates that the line is included in the solution set, and the region below the line is shaded.