Graphing Systems of 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 (>, <, ≥, ≤).

Front

What does a solid line represent in graphing linear inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (≥ or ≤).

Front

What does a dashed line represent in graphing linear inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (> 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 a linear inequality?

Back

The solution set is the set of all points that satisfy the inequality, represented graphically as a shaded region on the graph.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line divides the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Front

How do you graph a linear inequality in two variables?

Back

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

Front

What is a test point in graphing linear inequalities?

Back

A test point is a point used to determine which side of the boundary line to shade. (0,0) is often used if it is not on the line.

Front

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

Back

If a point lies on the boundary line and the line is solid, it is included in the solution set. If the line is dashed, it is not included.

Front

How can you tell if a point is part of the solution set for the inequality 5 ≥ x?

Back

The point is part of the solution set if its x-coordinate is less than or equal to 5.