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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 (>, <, ≥, ≤) instead of an equal sign.

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What does the solution set of a linear inequality represent?

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The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

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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 represents the solution set based on the inequality symbol.

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

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

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

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

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

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To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

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What is the significance of the shaded region in the graph of a linear inequality?

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The shaded region represents all the possible solutions to the inequality.

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What is the difference between a solution to a linear equation and a solution to a linear inequality?

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A solution to a linear equation is a specific point that makes the equation true, while a solution to a linear inequality includes a range of points that satisfy the inequality.

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If a point lies on a dotted line of a linear inequality, is it a solution?

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No, if a point lies on a dotted line, it is not included in the solution set.

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What does it mean if a point is above the line in a linear inequality graph?

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If a point is above the line in a linear inequality graph, it typically means that it satisfies the inequality (for y > mx + b type inequalities).