Enter Inequality Inputs
Use standard form ax + by relation c. The result appears above this form after submission.
Example Data Table
| Inequality | Boundary | x-intercept | y-intercept | Shaded Region |
|---|---|---|---|---|
| 2x + y ≤ 8 | Solid | (4, 0) | (0, 8) | Below the line |
| x - 3y > 6 | Dashed | (6, 0) | (0, -2) | Below the rewritten line |
| 4x + 0y ≥ 12 | Solid | (3, 0) | None | Right of the vertical line |
Formula Used
Linear inequalities in standard form use ax + by relation c. The calculator first draws the boundary line ax + by = c.
If b ≠ 0, the line can be rewritten as y relation (-a/b)x + c/b. The slope is -a/b and the y-intercept is c/b.
If a ≠ 0, the x-intercept is c/a. When the relation is < or >, the boundary is dashed. When the relation is ≤ or ≥, the boundary is solid.
The shaded region contains all points that satisfy the inequality. A quick check often uses the point (0, 0) when it is not on the boundary.
How to Use This Calculator
- Enter the coefficients for a, b, and c from your inequality.
- Select the correct relation sign: <, ≤, >, or ≥.
- Set the x and y viewing ranges for the graph window.
- Adjust the grid step for a smoother or faster shading display.
- Press Submit to show the result block above the form.
- Review the graph, intercepts, slope, boundary type, and test-point result.
- Use the export buttons to save the summary as CSV or PDF.