Unit 5: Flashcardziz #1 - 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 in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the symbol '≤' indicate in an inequality?

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. Then shade the appropriate region based on the inequality.

Front

What is the solution set of an inequality?

Back

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

Front

How can you determine if a point is part of the solution set for an inequality?

Back

To determine if a point is part of the solution set, substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the significance of a solid boundary line in graphing inequalities?

Back

A solid boundary line indicates that points on the line are included in the solution set, which corresponds to inequalities with '≥' or '≤'.

Front

What is the significance of a dashed boundary line in graphing inequalities?

Back

A dashed boundary line indicates that points on the line are not included in the solution set, which corresponds to inequalities with '>' or '<'.