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

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

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The symbol '>' means 'greater than'. It indicates that the values of the variable(s) must be greater than the value on the other side of the inequality.

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

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The symbol '<' means 'less than'. It indicates that the values of the variable(s) must be less than the value on the other side of the inequality.

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

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The symbol '≥' means 'greater than or equal to'. It indicates that the values of the variable(s) must be greater than or equal to the value on the other side of the inequality.

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

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The symbol '≤' means 'less than or equal to'. It indicates that the values of the variable(s) must be less than or equal to the value on the other side of the inequality.

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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 dashed line (for > or <). 2. Shade the region that satisfies the 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 can 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, 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 points on the line are included in the solution set (for ≥ or ≤). A dashed line indicates that points on the line are not included (for > or <).

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What is the slope-intercept form of a linear equation?

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