How to Graph Linear Inequalities

How to Graph Linear Inequalities

Learn how to graph linear inequalities using a testing point in few simple steps.

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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.

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

  • \(\color{blue}{y < – 4x + 2}\)
  • \(\color{blue}{2x + y < – 4}\)

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