Graphing Linear Inequalities Flashcard

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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 equal to or greater than the value on the other side of the inequality.

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

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The symbol '>' means 'greater than', indicating that the values of the variable must be strictly greater than the value on the other side of the inequality.

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

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The slope in a linear inequality 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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To determine which side to shade, pick a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing 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 the points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that the points on the line are not included (for < or >).

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What does the inequality @@y ge rac{4}{3}x - 1@@ represent graphically?

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

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