Graphing Linear Inequalities & Systems

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What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

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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 dashed (for < or >) or solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

Front

What does the shaded area in a graph of a linear inequality represent?

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The shaded area represents all the possible solutions to the inequality.

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered together.

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How do you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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

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If a point lies on the boundary line, it is a solution if the inequality includes equality (≤ or ≥). If the inequality is strict (< or >), the point is not 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 (≤ or ≥), while a dashed line indicates that points on the line are not included (< or >).

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How can you identify the solution set of a system of inequalities graphically?

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The solution set of a system of inequalities is the region where the shaded areas of all inequalities overlap.

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What is the significance of the slope in a linear inequality?

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The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).

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What does the y-intercept represent in the context of linear inequalities?

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The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.