Linear Inequalities & Systems of Linear Inequalities

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What is a linear inequality?

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A linear inequality is an inequality that involves a linear function, typically expressed in the form ax + by < c, ax + by ≤ c, ax + by > c, or ax + by ≥ c, where a, b, and c are constants.

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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 when graphing linear inequalities?

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

Tags

CCSS.HSA.REI.D.12

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

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The solution set of a system of linear inequalities represents all the points that satisfy all inequalities in the system simultaneously.

Tags

CCSS.HSA.REI.D.12

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How can you graph a linear inequality in two variables?

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To graph a linear inequality, first graph the corresponding linear equation as a line. Then, use a test point to determine which side of the line to shade, indicating the solution set.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the boundary line in a linear inequality?

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The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. The nature of the line (solid or dashed) indicates whether points on the line are included in the solution.

Tags

CCSS.HSA.REI.D.12

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What does the notation y ≥ -3 represent graphically?

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The notation y ≥ -3 represents all points on or above the horizontal line y = -3, including the line itself.

Tags

CCSS.HSA.REI.D.12

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What is a system of linear inequalities?

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A system of linear inequalities is a set of two or more linear inequalities that are considered together, and the solution is the intersection of the solution sets of each inequality.

Tags

CCSS.8.EE.C.8B

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How do you identify a point that is not a solution to a system of inequalities?

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To identify a point that is not a solution, substitute the point's coordinates into each inequality in the system. If the point does not satisfy at least one of the inequalities, it is not a solution.

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What is the role of test points in graphing linear inequalities?

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Test points are used to determine which side of the boundary line to shade when graphing a linear inequality. A point that satisfies the inequality indicates that the region containing that point is part of the solution set.

Tags

CCSS.HSA.REI.D.12