Graphing Linear Inequality

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What is a linear inequality?

Back

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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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). 2. Shade the region that satisfies 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 of the variable can be less than or equal to a certain number.

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

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The symbol '≥' means 'greater than or equal to', indicating that the values of the variable can be greater than or equal to a certain number.

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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. A positive slope means the line rises, while a negative slope means it falls.

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

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Choose a test point not on the line (commonly (0,0)). If the inequality holds true for that point, shade the side of the line that includes the test point.

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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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What is the general form of a linear inequality in two variables?

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How can you convert a linear inequality into slope-intercept form?

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What does it mean if a linear inequality has no solution?

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It means that there is no set of values that can satisfy the inequality, often represented by parallel lines that never intersect.