Linear Inequalities in Two Variables

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What is a linear inequality in two variables?

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What does the graph of a linear inequality represent?

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The graph of a linear inequality represents all the solutions (ordered pairs) that satisfy the inequality. It is typically a shaded region on one side of the boundary line.

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

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

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What does the slope-intercept form of a linear equation look like?

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a dashed or solid line. 2. Choose a test point (usually (0,0) if it's not on the line). 3. Substitute the test point into the inequality. If true, shade the side of the line where the test point is located; if false, shade the opposite side.

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What is the significance of the boundary line in a linear inequality?

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The boundary line in a linear inequality separates the solution set from the non-solution set. Depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥), the line may be dashed or solid.

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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 a solution if the inequality is inclusive (≤ or ≥) but not a solution if the inequality is strict (< or >).

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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 as a shaded region on the coordinate plane.

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How can you express a linear inequality in standard form?

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