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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

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

Back

The symbol '>' indicates that the values of the variable are greater than 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 are less than 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 are greater 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 are less than or equal to the value on the other side of the inequality.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

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.

Front

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

Back

Choose a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

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

Back

A dashed line indicates that points on the line are not included in the solution set (used for < or > inequalities).

Front

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

Back

A solid line indicates that points on the line are included in the solution set (used for ≤ or ≥ inequalities).