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 ≥.

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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 does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the values of the variable can be less than or equal to the value on the other side of the inequality.

Front

What does the symbol '>' indicate in a linear inequality?

Back

The symbol '>' indicates that the values of the variable must be greater than the value on the other side of the inequality.

Front

Back

A dashed line is used because the inequality does not include equality.

Front

When graphing the inequality @@y eq -x - 4@@, what type of line is used?

Back

A dashed line is used because the inequality does not include equality.

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 (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

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How can you determine if a point is a solution to a linear inequality?

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

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, represented graphically by the shaded region on the graph.

Front

What does the term 'boundary line' refer to in the context of linear inequalities?

Back

The boundary line is the line that represents the corresponding linear equation of the inequality, which divides the plane into two regions.