Read: Graph an Inequality in Two Variables
Learning Objectives
- Identify and follow steps for graphing a linear inequality in two variables
Graphing Inequalities
To graph an inequality:- Graph the related boundary line. Replace the <, >, ≤ or ≥ sign in the inequality with = to find the equation of the boundary line.
- Identify at least one ordered pair on either side of the boundary line and substitute those values into the inequality. Shade the region that contains the ordered pairs that make the inequality a true statement.
- If points on the boundary line are solutions, then use a solid line for drawing the boundary line. This will happen for ≤ or ≥ inequalities.
- If points on the boundary line aren’t solutions, then use a dotted line for the boundary line. This will happen for < or > inequalities.
x | y |

This is a false statement, since is not less than or equal to . On the other hand, if you substitute into :
This is true! The region that includes should be shaded, as this is the region of solutions.

Graphing Linear Inequalities in Two Variables
https://youtu.be/2VgFg2ztspIExample
Graph the inequality .Answer: Solve for y.
Create a table of values to find two points on the line , or graph it based on the slope-intercept method, the b value of the y-intercept is and the slope is . Plot the points, and graph the line. The line is dotted because the sign in the inequality is >, not ≥ and therefore points on the line are not solutions to the inequality.

x | y |
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Answer
The graph of the inequality is: