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 shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality, indicating where the inequality holds true.

Front

What is the significance of a dotted line in the graph of a linear inequality?

Back

A dotted line indicates that points on the line are not included in the solution set (for inequalities using < 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 (for inequalities using ≤ 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 slope of a line?

Back

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (dotted or solid). 2. Choose a test point not on the line. 3. Shade the region that satisfies the inequality.

Front

What is the difference between a solution set and a boundary line in linear inequalities?

Back

The solution set includes all points that satisfy the inequality, while the boundary line separates the solution set from the non-solution set.

Front

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

Back

If the boundary line is solid, the point is included in the solution set. If the line is dotted, the point is not included.

Front

What is the purpose of using test points in graphing linear inequalities?

Back

Test points help determine which side of the boundary line to shade, indicating where the solutions to the inequality lie.