Graphing Linear Inequalities

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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 (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

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How do you graph a linear inequality?

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1. Start by graphing the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Choose a test point not on the line to determine which side of the line to shade. 3. Shade the region that satisfies the inequality.

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What does the symbol '>' mean in a linear inequality?

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Front

What does the symbol '<' mean in a linear inequality?

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What does the symbol '≥' mean in a linear inequality?

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What does the symbol '≤' mean in a linear inequality?

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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. It is represented graphically as a shaded region on the coordinate plane.

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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 to a linear inequality, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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

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How can you convert a linear inequality into slope-intercept form?

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