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 (e.g., <, >, ≤, ≥).

Front

What does the shaded region represent in a graph of a linear inequality?

Back

The shaded region represents all the possible solutions to the inequality.

Front

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

Back

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

Front

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

Back

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

Front

How do 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, the point is a solution.

Front

What is the solution set of the inequality y ≤ 5x - 1?

Back

The solution set includes all points (x, y) that lie on or below the line y = 5x - 1.

Front

Which of the following points is a solution for the inequality y ≤ 5x - 1: (7, 1), (5, 3), (0, -5), (1, 7)?

Back

(0, -5) is a solution because it lies below the line.

Front

What is the significance of the inequality symbol in a linear inequality?

Back

The inequality symbol indicates the relationship between the two expressions, determining whether one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

How can you graph the inequality y > 2x + 3?

Back

Graph the line y = 2x + 3 with a dashed line and shade the region above the line.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as if it were an equality.