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

How do you graph a linear inequality?

Back

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

Front

What does a dashed line indicate in a graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict: < or >).

Front

What does a solid line indicate in a graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict: ≤ or ≥).

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is part of the solution set.

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

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

Back

The symbol '>' means that the value on the left is greater than the value on the right, and the points on the line are not included in the solution.

Front

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

Back

The symbol '<' means that the value on the left is less than the value on the right, and the points on the line are not included in the solution.

Front

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

Back

The symbol '≥' means that the value on the left is greater than or equal to the value on the right, and the points on the line are included in the solution.

Front

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

Back

The symbol '≤' means that the value on the left is less than or equal to the value on the right, and the points on the line are included in the solution.