Graphing Linear Inequalities

Front

What is a linear inequality?

Back

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

Front

What does the symbol '≥' indicate when graphing?

Back

The symbol '≥' indicates that the line is solid and the region above the line is shaded, representing all points where the inequality holds true.

Front

What does the symbol '≤' indicate when graphing?

Back

The symbol '≤' indicates that the line is solid and the region below the line is shaded, representing all points where the inequality holds true.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

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 >).

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region on the graph.

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

Back

If a point lies on the boundary line of a linear inequality, it is included in the solution set if the line is solid (for ≤ or ≥) and not included if the line is dashed (for < or >).

Front

What is a test point in the context of graphing inequalities?

Back

A test point is a specific point used to determine which side of the boundary line to shade when graphing a linear inequality.

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