Enter graph settings
Example data table
| Inequality | Meaning | Boundary type | Region kept |
|---|---|---|---|
| x + y ≤ 6 | Points on or below the line x + y = 6 | Solid | Below the boundary |
| x − y ≥ 0 | Points where x is at least y | Solid | Below or on y = x |
| y ≥ -2 | Points above or on the horizontal boundary | Solid | Above the boundary |
Formula used
Standard linear inequality form: ax + by relation c
Boundary line: ax + by = c
Slope: m = -a / b, when b ≠ 0
x-intercept: x = c / a, when a ≠ 0 and y = 0
y-intercept: y = c / b, when b ≠ 0 and x = 0
Feasibility test: A point (x, y) is included when each inequality remains true after substitution.
The graph window is clipped by each half-plane. The visible solution region is the shared overlap that survives every clipping step.
How to use this calculator
- Enter a graph title, test point, and visible x and y ranges.
- Enable one to three inequalities in the form ax + by relation c.
- Choose solid boundaries for inclusive symbols and dashed boundaries for strict symbols.
- Press Plot Inequalities to draw the graph and calculate visible overlap.
- Review intercepts, slopes, boundary types, test point results, and feasible vertices.
- Use the export buttons to save the summary as CSV or PDF.
FAQs
1. What does the shaded area represent?
The shaded area shows every point that satisfies all enabled inequalities together. If no shared area exists inside the chosen window, the graph reports no visible feasible region.
2. Why are some boundaries dashed?
Dashed boundaries appear for strict symbols such as < or >. Those lines mark limits that points may approach, but not include, in the final solution set.
3. Why can the feasible area be zero?
Zero area usually means the inequalities conflict, or the shared solution collapses into a line or single point within the current graph window.
4. Does the calculator support vertical lines?
Yes. When b equals zero, the boundary becomes vertical, the slope is undefined, and the graph still plots the line correctly using x = c / a.
5. What is the test point used for?
The test point lets you check one coordinate pair against every inequality. It is useful for verifying whether a proposed answer belongs inside the feasible region.
6. Why does changing the window change the area?
The area is measured only inside the current viewing box. An unbounded solution may look finite because the calculator clips it to your selected x and y limits.
7. Can I graph one inequality only?
Yes. Enable just one inequality and disable the others. The graph will then display the single half-plane, its boundary, and the selected test point result.
8. What do the intercept values mean?
Intercepts show where the boundary line crosses each axis. They help you sketch the line quickly and understand how the inequality shapes the graph.