Green Bridge Learning Resource For Graph Solutions To Linear Inequalities In Two Variables

Overview

A linear inequality in two variables does not have a single solution: it has a whole region of points that satisfy it. Shading that region turns the inequality into a picture, which is exactly how solutions are shown and combined.

In this lesson you will graph the solution to a linear inequality in two variables as a half-plane (region), and decide whether the boundary line is included.

Lesson Evaluation

Congratulations on completing the lesson on Graph Solutions To Linear Inequalities In Two Variables. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

The solution of a linear inequality in two variables is: A. one point B. a line C. a half-plane (region) D. a curve Answer: C
For a strict inequality (>), the boundary line is drawn: A. solid B. dashed C. doubled D. not at all Answer: B
For y <= x + 1, the boundary line is drawn: A. dashed B. solid C. wavy D. red Answer: B
To decide which side to shade you use a: A. ruler B. test point C. protractor D. tangent Answer: B
Testing (0, 0) in y > x + 1 gives 0 > 1, which is false, so you shade: A. the side containing the origin B. the side not containing the origin C. both sides D. neither side Answer: B