Understanding linear inequalities in two variables

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What is a linear inequality in two variables?

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

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A point (x, y) is a solution of a linear inequality if, when substituted into the inequality, it makes the inequality true.

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What is a non-solution point in the context of linear inequalities?

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A non-solution point is a point that does not satisfy the linear inequality when substituted into it.

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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 and check if the inequality holds true.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a region on the coordinate plane, often bounded by a dashed or solid line, indicating all the solutions to the inequality.

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

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

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

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

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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 coordinates of the point into the inequality. If the inequality is true, the point is in the solution set.