Calculator Inputs
Plotly Graph
Example Data Table
| Example | Inequality 1 | Inequality 2 | Combine Mode | Window | Interpretation |
|---|---|---|---|---|---|
| Feasible budgeting region | x + y ≤ 6 | -x + y ≥ -1 | AND | x: -2 to 8, y: -2 to 8 | The shared shaded region satisfies both limits together. |
| Single half-plane | 2x - y < 4 | Not used | Single | x: -10 to 10, y: -10 to 10 | The graph shades one side of the dashed boundary. |
| Vertical boundary | x ≥ 3 | Not used | Single | x: -1 to 8, y: -6 to 6 | A solid vertical line appears because equality is included. |
| Union region | y > x - 2 | y < -x + 5 | OR | x: -8 to 8, y: -8 to 8 | Points satisfying either inequality are kept in the solution. |
Formula Used
Each inequality uses the standard linear form ax + by [operator] c. The matching boundary line comes from replacing the inequality symbol with an equals sign, giving ax + by = c.
Boundary line: ax + by = c
Slope form when b ≠ 0: y = (c - ax) / b
x-intercept: x = c / a when a ≠ 0
y-intercept: y = c / b when b ≠ 0
Region test: A point belongs to the shaded half-plane when its coordinates make the inequality true.
Strict signs (< or >) use dashed boundaries. Inclusive signs (≤ or ≥) use solid boundaries. When two inequalities are enabled, AND shades the intersection, while OR shades the union.
How to Use This Calculator
- Enter coefficients for the first inequality in the form ax + by [operator] c.
- Choose the correct comparison symbol to define the shaded side.
- Enable the second inequality if you need an intersection or union.
- Set the x and y viewing window for the graph.
- Adjust the sampling grid size for a faster or finer estimate.
- Add a test point if you want to verify a specific coordinate pair.
- Press the button to display the result above the form.
- Use the CSV and PDF buttons to export the summary.
Frequently Asked Questions
1. What type of inequalities can this page graph?
It graphs linear inequalities written as ax + by [operator] c. This includes horizontal lines, sloped lines, and vertical boundaries when b equals zero.
2. Why are some boundaries dashed?
Dashed boundaries appear for strict inequalities such as < or >. They show that points on the boundary line itself are excluded from the solution set.
3. Why are some boundaries solid?
Solid boundaries appear for ≤ or ≥. They indicate the boundary line is included, so points exactly on the line satisfy the inequality.
4. What does the coverage percentage mean?
Coverage percentage estimates how much of the chosen viewing window satisfies the inequality set. It depends on the graph range and the selected sampling density.
5. What is the combine mode used for?
AND keeps only points satisfying both inequalities. OR keeps points satisfying at least one inequality. This helps model feasible regions or unions of half-planes.
6. Can I use a test point?
Yes. Enter any coordinate pair and enable the test point option. The result summary tells you whether that point lies inside the final shaded region.
7. Why does the approximate area change?
The estimate depends on the viewing window and grid density. A larger grid samples more points and generally gives a smoother, more refined estimate.
8. Can this help with algebra homework and optimization setup?
Yes. It is useful for checking shading direction, intercepts, feasible regions, and boundary styles before solving systems or graph-based optimization problems.