Linear Inequality Graphing Guide
A linear inequality shows a half plane. Its boundary is a straight line. The line comes from replacing the inequality sign with an equal sign. The calculator converts each rule into standard form, ax + by = c. It then finds slope, intercepts, and the side that should be shaded. This makes the graph easier to read.
Why This Tool Helps
Manual graphing can be slow when several inequalities appear together. You must draw every boundary, check strict signs, test sample points, and find the overlap. This calculator keeps those steps in one place. It reports the boundary type, the shading direction, and whether your test point satisfies each rule. It also estimates the shared feasible region on the canvas.
Important Graph Details
The sign controls the boundary. Less than or greater than signs create dashed lines. Less than or equal to signs create solid lines. Greater than or equal to signs also create solid lines. A vertical boundary appears when b is zero. A horizontal boundary appears when a is zero. Both cases are handled without changing your equation format.
Using Test Points
A test point is useful because it confirms the shaded side. The common point is (0, 0), but it may sit on a boundary. You may enter any point. The calculator substitutes your x and y values into every inequality. It then compares the left side with the right side. This gives a quick pass or fail result.
Practical Uses
Students can use this tool for algebra, coordinate geometry, and linear programming tasks. Teachers can prepare examples and export tables for lessons. Business users can model capacity limits, budget limits, and production constraints. The graph is not a formal proof. It is a clear visual aid. Use exact algebra for final answers when precision matters.
Exporting Work
The CSV button saves the computed rows. The PDF button captures the main summary. These exports help when you need to keep homework steps, compare scenarios, or share calculations with others. Adjust the window values when the graph looks cramped. Wider ranges show distant intercepts. Narrower ranges reveal local overlap. Enter clean coefficients for best results. Review each line before exporting your final worksheet. Keep axes visible.