Linear inequalities (two variables)

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What is a linear inequality in two variables?

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What does the shaded area represent in a graph of a linear inequality?

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The shaded area represents all the possible solutions to the linear inequality. Points in the shaded area satisfy the inequality.

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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 (x, y) is a solution, substitute the x and y values into the inequality. If the inequality holds true, the point is a solution.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

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What does it mean if a point is excluded from the solution set of a linear inequality?

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If a point is excluded, it means that when the coordinates of the point are substituted into the inequality, the inequality does not hold true.

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How can 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 appropriate region based on the inequality.

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

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The boundary line represents the points where the inequality changes from true to false. It is included in the solution set for non-strict inequalities.

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