Solutions to Linear Inequalities Flashcard

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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 (>, <, ≥, ≤).

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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 or solid line, then shade the region that satisfies the inequality.

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What does it mean for a point to be a solution to a linear inequality?

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A point is a solution to a linear inequality if it lies in the shaded region of the graph of 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 (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

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How can you determine if a point is a solution to a linear inequality?

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Substitute the x and y coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

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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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How do you test if a point is in the solution set of an inequality?

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Substitute the point's coordinates into the inequality. If the resulting statement is true, the point is in the solution set.

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What is the significance of the y-intercept in a linear inequality?

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The y-intercept is the point where the line crosses the y-axis, which helps in graphing the inequality.

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What does it mean if a point is NOT part of the solution set?

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It means that the point does not satisfy the inequality when its coordinates are substituted into it.