How to Put Inequality in Graphing Calculator

Graphing inequalities on a graphing calculator is a fundamental skill in algebra and calculus. This guide explains how to properly input and interpret inequality graphs using popular calculator models like TI-84, Desmos, and GeoGebra.

Basic Steps to Graph Inequalities

To graph an inequality in your calculator, follow these essential steps:

Enter the equation: Type the equation without the inequality sign (e.g., y = 2x - 3)
Set the window: Adjust the graphing window to show the relevant area
Graph the line: Use the line graphing mode
Shade the area: Use the inequality symbol to determine which side to shade
Test a point: Verify the shading by testing a point not on the line

Note: The inequality symbol (≤, ≥, <, >) determines which side of the line to shade. Always test a point to confirm your shading.

Example: Graphing y > 2x - 3

Let's walk through a complete example:

Enter the equation: y = 2x - 3
Set the window: Xmin = -5, Xmax = 5, Ymin = -5, Ymax = 5
Graph the line using the line mode
Since the inequality is "greater than" (>), shade above the line
Test (0,0): 0 > 2(0) - 3 → 0 > -3 (True) confirms shading is correct

Formula: For y > mx + b, shade above the line if the inequality is "greater than" or below if "less than".

Common Mistakes to Avoid

When graphing inequalities, avoid these common errors:

Forgetting to remove the inequality sign when entering the equation
Shading the wrong side of the line based on the inequality symbol
Not testing a point to verify the shading
Using the wrong graphing mode (solid line instead of dashed)
Not adjusting the window to show the relevant area

Calculator-Specific Tips

TI-84 Family

Use the Y= editor to enter the equation
Set the mode to "Dot" for dashed lines
Use the Shade Above/Below feature in the Graph menu

Desmos

Enter the equation with the inequality symbol
Desmos automatically shades the correct area
Use the slider feature to adjust variables

GeoGebra

Enter the equation in the input bar
Use the "Inequality" tool to shade regions
Adjust the view with the zoom tools

Frequently Asked Questions

Can I graph inequalities with two variables?: Yes, but you'll need to graph them as systems of inequalities. Most graphing calculators can handle this.
What if my inequality has absolute value?: Break it into two separate inequalities (e.g., |x| > 3 becomes x > 3 or x < -3) and graph each one.
How do I graph inequalities with parameters?: Use your calculator's parameter feature to adjust values and see how the graph changes.
Why is my shading not showing up?: Check that you've selected the correct shading option in your calculator's menu and that the window is set properly.