Solutions to Linear Inequalities

Front

What does a dashed or dotted line represent in a linear inequality?

Back

A dashed or dotted line indicates that the points on the line are NOT included in the solution set.

Front

Are points on a solid line part of the solution set in a linear inequality?

Back

Yes, points on a solid line are included in the solution set.

Front

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

Back

A point is a solution if it lies in the shaded region of the graph representing the inequality.

Front

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

Back

The shaded region represents all the solutions to the inequality.

Front

If a linear inequality is represented by a dotted line, what can you say about the points on that line?

Back

The points on a dotted line are NOT part of the solution set.

Front

What is the solution set of the inequality y < 2x + 3?

Back

The solution set includes all points below the line y = 2x + 3, excluding the line itself.

Front

Which of the following points is a solution to the inequality y > -x + 1? (0, 2), (1, 0), (-1, 3)

Back

(0, 2) is a solution because it lies above the line y = -x + 1.

Front

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

Back

The inequality symbol indicates the relationship between two expressions and determines the solution set.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation. 2. Use a solid line for ≤ or ≥ and a dashed line for < or >. 3. Shade the appropriate region.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If the line is solid, the point is included in the solution set; if the line is dashed, the point is not included.