Graph Linear Inequalities In Two Variables

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What is a linear inequality in two variables?

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A linear inequality in two variables is an inequality that can be expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.

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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, often depicted as a shaded region on a graph.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dotted line (for < or >). 2. Shade the appropriate region based on the inequality.

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

Back

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

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

Back

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

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How can you determine which side of the line to shade when graphing a linear inequality?

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You can test a point not on the line (like (0,0)) in the inequality. If the inequality holds true, shade the side containing that point.

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What is the significance of the inequality symbol in determining the type of line used in graphing?

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The inequality symbol determines whether the line is solid or dotted: < or > results in a dotted line, while ≤ or ≥ results in a solid line.

Front

If the inequality is y < 2x + 3, what type of line will be used?

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A dotted line will be used, and the shading will be below the line.

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What does it mean if a point lies on the line of a linear inequality?

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If a point lies on the line of a linear inequality, it is part of the solution set only if the line is solid (for ≤ or ≥). If the line is dotted, the point is not included.

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What is the first step in solving a linear inequality?

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The first step is to isolate the variable on one side of the inequality, similar to solving an equation.