Graph The Following Inequality Calculator

This calculator helps you graph linear inequalities on a coordinate plane. Whether you're studying algebra or need a quick reference, this tool will help you visualize the solution to any linear inequality.

How to Use This Calculator

To graph an inequality using this calculator:

Enter the coefficients for x and y in the inequality (e.g., 2x + 3y > 6)
Select the inequality type (greater than, less than, etc.)
Click "Graph Inequality" to see the solution on the coordinate plane
Review the step-by-step solution and interpretation

Tip: The calculator will automatically adjust the graph scale to fit your inequality. For best results, keep the coefficients between -10 and 10.

How the Calculator Works

The calculator uses the following steps to graph linear inequalities:

First, solve the corresponding equation (replace the inequality with an equals sign)
Graph the line using the slope-intercept form (y = mx + b)
Determine which side of the line satisfies the inequality
Shade the appropriate region of the coordinate plane

For an inequality of the form Ax + By > C:

Solve for y: y > (-A/B)x + (C/B)
Graph the line y = (-A/B)x + (C/B)
Shade above the line if B is positive, below if B is negative

Worked Examples

Example 1: Simple Inequality

Graph the inequality: 2x + 3y > 6

First solve the equation: 2x + 3y = 6
Find the x-intercept: set y=0 → 2x=6 → x=3
Find the y-intercept: set x=0 → 3y=6 → y=2
Graph the line through (3,0) and (0,2)
Shade above the line since the inequality is "greater than"

Example 2: Negative Coefficients

Graph the inequality: -x + 2y < 4

First solve the equation: -x + 2y = 4
Find the x-intercept: set y=0 → -x=4 → x=-4
Find the y-intercept: set x=0 → 2y=4 → y=2
Graph the line through (-4,0) and (0,2)
Shade below the line since the inequality is "less than"

Frequently Asked Questions

What types of inequalities can this calculator graph?: This calculator can graph linear inequalities with two variables (x and y) using the standard inequality symbols (>, <, ≥, ≤).
How do I interpret the shaded region?: The shaded region represents all the points (x,y) that satisfy the original inequality. The line itself is drawn as a dashed line to indicate it's not included in the solution.
Can I graph inequalities with fractions or decimals?: Yes, the calculator accepts any real number coefficients. Just enter them as you would in the inequality.
What if my inequality doesn't have a y-intercept?: The calculator will still work. If there's no y-intercept, the line will be vertical. The shading will be to the left or right of the line depending on the inequality.