Graphing Linear Inequalities

Front

What is a linear inequality?

Back

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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How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.

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

Back

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

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

Back

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

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

Back

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

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

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An inequality will have a solid line if it includes 'or equal to' (i.e., it uses ≤ 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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What does the symbol '≤' mean in a linear inequality?

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The symbol '≤' means 'less than or equal to', indicating that the values on the line are included in the solution set.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the values on the line are included in the solution set.

Front

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

Back

To determine which side to shade, pick a test point (usually (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.