Graph Systems of Linear Inequalities

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What is a linear inequality?

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

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What does the solution of a system of linear inequalities represent?

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The solution of a system of linear inequalities represents all the points (x, y) that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

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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 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 is the significance of the intersection of shaded regions in a graph of inequalities?

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The intersection of shaded regions represents the set of solutions that satisfy all inequalities in the system.

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

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How do you find the y-intercept of a linear inequality?

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