How to Graph Linear Inequalities? (+FREE Worksheet!)
Learn how to graph linear inequalities using a testing point in a few simple steps.
Related Topics
- How to Find Midpoint
- How to Find Distance of Two Points
- How to Find Slope
- How to Write Linear Equations
- How to Graph Lines by Using Standard Form
Step by step guide to graphing linear inequalities
- First, graph the “equals” line.
- Choose a testing point. (it can be any point on both sides of the line.)
- Put the value of \((x, y)\) of that point in the inequality. If that works, that part of the line is the solution. If the values don’t work, then the other part of the line is the solution.
The Absolute Best Books to Ace Pre-Algebra to Algebra II
Graphing Linear Inequalities – Example 1:
Sketch the graph of \(y<2x-4\).
Solution:
First, graph the line:
\(y=2x-4\). The slope is \(2\) and \(y\)-intercept is \(-4\).
Then, choose a testing point. The easiest point to test is the origin: \((0,0)\)
\((0,0)→y<2x-4→0<2(0)-4→0<-4\)
\(0\) is not less than \(-4\). So, the other part of the line (on the right side) is the solution.
Graphing Linear Inequalities – Example 2:
Sketch the graph of \(y<2x-3\).
Solution:
First, graph the line:
\(y=2x-3\). The slope is \(2\) and \(y\)-intercept is \(-3\).
Then, choose a testing point. The easiest point to test is the origin: \((0,0)\)
\((0,0)→y<2x-3→0<2(0)-3→0<-3\)
\(0\) is not less than \(-3\). So, the other part of the line (on the right side) is the solution.
Exercises for Graphing Linear Inequalities
Sketch the graph of each linear inequality.
- \(\color{blue}{y < – 4x + 2}\)
- \(\color{blue}{2x + y < – 4}\)
Download Graphing Linear Inequalities Worksheet
- \(\color{blue}{y < – 4x + 2}\)
- \(\color{blue}{2x + y < – 4}\)
The Greatest Books for Students to Ace the Algebra
Related to This Article
More math articles
- How to Use the Distributive Property? (+FREE Worksheet!)
- Top 5 Free Websites for ASTB-E Math Preparation
- Full-Length 6th Grade PSSA Math Practice Test-Answers and Explanations
- How to Modeling Real-World Situations Using Functions
- Discovering the Magic of SSS and SAS Congruence in Triangles
- Find the Key: “AFOQT Math for Beginners” Complete Answer Book
- How to Identify an Outlier
- How to Use Benchmark Fraction? Benchmark Fraction Definition
- Unraveling More about Limits at Infinity
- The Ultimate ASVAB Math Course (+FREE Worksheets & Tests)
What people say about "How to Graph Linear Inequalities? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.