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 a linear inequality?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

How do you graph a linear inequality with '>' or '<'?

Back

You graph a linear inequality with '>' or '<' using a dotted line to indicate that points on the line are not included in the solution.

Front

How do you graph a linear inequality with '≥' or '≤'?

Back

You graph a linear inequality with '≥' or '≤' using a solid line to indicate that points on the line are included in the solution.

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 of the line to shade when graphing a linear inequality?

Back

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

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., y = mx + b), while a linear inequality shows a relationship of inequality (e.g., y < mx + b).