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 (>, <, ≥, ≤).

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the specified number.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to the specified number.

Front

How do you graph a linear inequality?

Back

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 is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

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What does it mean if a point is part of the solution set of a linear inequality?

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If a point is part of the solution set, it means that when the coordinates of the point are substituted into the inequality, the statement is true.

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How can you determine if a point is in the solution set of a linear inequality?

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To determine if a point is in the solution set, substitute the x and y values of the point into the inequality and check if the inequality holds true.

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

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

Front

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

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The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

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How do you convert a linear inequality to slope-intercept form?

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To convert a linear inequality to slope-intercept form, isolate y on one side of the inequality.