Linear Inequalities & Graphs

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What is a linear inequality?

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A linear inequality is a mathematical statement that relates 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 that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

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What is the difference between < and ≤ in linear inequalities?

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The symbol < indicates that the value is strictly less than, while ≤ indicates that the value can be less than or equal to.

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What does the dashed line in a graph of a linear inequality indicate?

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A dashed line indicates that the points on the line are not included in the solution set (for inequalities using < or >).

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What does the solid line in a graph of a linear inequality indicate?

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A solid line indicates that the points on the line are included in the solution set (for inequalities using ≤ or ≥).

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How do you determine which side of the line to shade in a linear inequality?

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You can test a point not on the line (commonly (0,0)) in the inequality. If the inequality holds true, shade the side containing that point.

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What is the solution set of the inequality @@y eq 3x + 1@@?

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

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The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).