Graphing Linear Inequalities

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What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

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, which can be visualized as a shaded region on a graph.

Front

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 ≥), while a dashed line indicates that points on the line are not included (for < or >).

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

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What is the standard form of a linear inequality?

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The standard form of a linear inequality is typically written as 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 symbol '>' mean in a linear inequality?

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The symbol '>' means that the expression on the left side is greater than the expression on the right side, indicating that the values satisfying the inequality are above a certain threshold.

Front

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

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The symbol '≤' means that the expression on the left side is less than or equal to the expression on the right side, indicating that the values satisfying the inequality include the boundary.

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How do you convert a linear equation to a linear inequality?

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To convert a linear equation to a linear inequality, replace the equality sign (=) with an inequality symbol (<, >, ≤, or ≥) based on the context of the problem.

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What is the significance of the boundary line in graphing linear inequalities?

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The boundary line in graphing linear inequalities separates the solution set from the non-solution set, indicating which side of the line contains the solutions.