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 the symbol '≥' indicate in a linear inequality?

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The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

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What does the symbol '≤' indicate in a linear inequality?

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The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a boundary line. 2. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. 3. Shade the region that satisfies 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 tell if an inequality will have a solid boundary line?

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An inequality will have a solid boundary line if it includes 'or equal to' (≥ or ≤).

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How can you tell if an inequality will have a dashed boundary line?

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An inequality will have a dashed boundary line if it does not include 'or equal to' (> or <).

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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.

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