Graphing Linear Inequalities

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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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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then 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 '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 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 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 do you determine which side of the line to shade when graphing a linear inequality?

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To determine which side to shade, pick a test point not on the line (commonly (0,0)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side containing the test point.

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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, represented graphically by the shaded region on the graph.

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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 point lies on the boundary line of a linear inequality?

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If a point lies on the boundary line of a linear inequality, it is included in the solution set if the line is solid (for ≤ or ≥) and not included if the line is dashed (for < or >).