Linear Inequalities on a Graph
Shade the half-plane that satisfies the inequality.
About this topic
A linear inequality like y > 2x − 1 has a whole region of solutions. Graph the boundary line first, drawing it dashed for less than or greater than and solid for less than or equal to or greater than or equal to, then shade the side that makes the inequality true. Test a point such as the origin to decide which side.
A system of inequalities is graphed by shading each one; the solution is the overlapping region where all are true. For y > 2x − 1, testing (0, 0) gives 0 > −1, which is true, so you shade the side containing the origin. If the boundary passes through the origin, pick a different test point.
This idea powers linear programming, which businesses use to maximize profit or minimize cost under limits on time, money and materials. A diet plan, a factory schedule or a budget all give a feasible region where the answer must lie.
Typical errors are using a solid line when the points on the line are not solutions, and forgetting to reverse the inequality sign when dividing by a negative number while solving for y.
Key ideas
- Solid line for ≤ or ≥, dashed for < or >
- Test a point to choose the side
- Systems shade the overlap
Quick check
Use cases: where Linear Inequalities on a Graph helps
- Homework: review the key idea behind Linear Inequalities on a Graph before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Linear Inequalities on a Graph without notes.
- Visual learning: play with the interactive lab to see how Linear Inequalities on a Graph changes when you adjust its inputs.
- Teaching a friend: explain Linear Inequalities on a Graph in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Linear Inequalities on a Graph?
Shade the half-plane that satisfies the inequality.
What will I learn in Linear Inequalities on a Graph?
Solid line for ≤ or ≥, dashed for < or >. Test a point to choose the side. Systems shade the overlap.
Is Linear Inequalities on a Graph part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Linear Inequalities on a Graph lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Linear Inequalities on a Graph?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.