Inputs
Higher values render smoother shading.
Results Table
| # | Input | A | B | C | Sign | Boundary | x-intercept | y-intercept |
|---|
Standard form shown as A·x + B·y (sign) C.
Example Data
Click “Load” to try a preset set.
| Preset name | Inequalities | |
|---|---|---|
| Triangle region | y <= 2x + 3; y >= -x - 2; x >= -1 | |
| Band between lines | y > -0.5x - 1; y < 0.5x + 2 | |
| Vertical and horizontal | x <= 4; y >= -3 |
Formulas Used
- Normalize each inequality to A·x + B·y (sign) C.
- Boundary line: if B ≠ 0, slope-intercept is y = -(A/B)x + C/B.
- Vertical line: if B = 0, boundary is x = C/A.
- Intersections satisfy all inequalities simultaneously (logical AND).
- Strict signs (< or >) draw dashed boundaries; non-strict use solid.
Feasible region shading is computed by testing grid points against all constraints.
How to Use
- Enter inequalities like
2x + 3y <= 6,y > -x + 2, orx >= -1. - Ranges control the visible window for x and y axes.
- Click Plot to draw boundaries and shade the feasible region.
- Review normalized coefficients and intercepts in the results table.
- Use Download CSV or Download PDF to save your work.
For best results, keep inputs linear in x and y only.
FAQs
Use linear forms such as
ax + by <= c, y > mx + b, or x >= k. Parentheses and products are not supported.A grid of points is tested against all inequalities. Points that satisfy every constraint are shaded as the feasible region.
Solid boundaries represent ≤ or ≥, meaning the line is included. Dashed boundaries represent < or >, meaning the line is excluded.
Yes. Use forms like
x <= 4 or x > -2. Vertical boundaries are handled explicitly.The parser accepts only linear combinations of x and y. Remove parentheses, products, and powers, and ensure coefficients and constants are numbers.
Supported Input Patterns (Normalized)
| Inequality | A | B | C | Sign | Boundary | x-intercept | y-intercept |
|---|---|---|---|---|---|---|---|
2x + 3y <= 6 | 2 | 3 | 6 | ≤ | solid | 3 | 2 |
y >= -x + 2 | 1 | 1 | 2 | ≥ | solid | 2 | 2 |
x <= 4 | 1 | 0 | 4 | ≤ | solid | 4 | — |
y > 0.5x - 1 | -0.5 | 1 | -1 | > | dashed | 2 | -1 |
-x + y <= 3 | -1 | 1 | 3 | ≤ | solid | -3 | 3 |
3x - 2y >= -6 | 3 | -2 | -6 | ≥ | solid | -2 | 3 |
Normalization uses A·x + B·y (sign) C. Intercepts shown where applicable.
Defaults & Output Data
| Setting | Value | Notes |
|---|---|---|
| Axis ranges | x: -10 to 10; y: -10 to 10 | Adjust in Inputs → Ranges. |
| Grid resolution | 101 | Higher values make smoother shading. |
| Line samples | 400 | More points give smoother boundaries. |
| Shade intersection only | On | Toggle to view per-inequality shading. |
| Palette size | 10 colors | Cycles through distinct line colors. |
| CSV filename | graphing_inequalities_results.csv | Includes coefficients, signs, and intercepts. |
| PDF filename | graphing_inequalities_report.pdf | Embeds the current plot and inequalities list. |
| Numeric tolerance | 1e-12 | Used for comparisons to reduce jitter. |
| Supported signs | ≤, <, ≥, > | Unicode aliases map to standard operators. |
| Variables | x, y | Linear terms only; no products/powers. |