Calculator Inputs
Example Data Table
| Inequality | Boundary type | Typical shading | Test point | Outcome |
|---|---|---|---|---|
| x + y ≤ 4 | Solid | Below the line | (0, 0) | Satisfies |
| 2x - y > 3 | Dashed | Below the rearranged line | (1, 1) | Does not satisfy |
| x ≥ -2 | Solid vertical | Right of the boundary | (0, 5) | Satisfies |
| y < 3 | Dashed horizontal | Below the boundary | (0, 4) | Does not satisfy |
Formula Used
General boundary line: A x + B y = C
Inequality region: A x + B y < C, A x + B y ≤ C, A x + B y > C, or A x + B y ≥ C
Slope of boundary: m = -A / B, when B is not zero
x-intercept: x = C / A, when A is not zero
y-intercept: y = C / B, when B is not zero
Test point rule: Substitute a chosen point (x₀, y₀) into A x₀ + B y₀. Compare that value with C using the selected sign.
Boundary rule: Use a solid line for ≤ or ≥. Use a dashed line for < or >.
How to Use This Calculator
- Enter the coefficients A, B, and C for the inequality A x + B y relation C.
- Select the inequality sign that matches your problem.
- Set graph window limits for x and y.
- Choose a grid step and decimal precision.
- Enter a test point to check whether it belongs to the solution region.
- Press Shade Inequality to display the graph and computed summary.
- Review the intercepts, solved form, boundary style, and shading guide.
- Use the export buttons to save the result as CSV or PDF.
FAQs
1. What does the shaded region represent?
It represents every point that satisfies the selected inequality. Any coordinate inside the shaded region makes the inequality true when substituted into the left side.
2. Why is the boundary line sometimes dashed?
A dashed line means boundary points are excluded. That happens for strict inequalities, such as < or >, because points exactly on the line do not satisfy the statement.
3. Why is the boundary line solid for ≤ and ≥?
A solid line means boundary points are included. Points on the line make the two sides equal, so they belong to the solution set for inclusive inequalities.
4. What happens if B equals zero?
The boundary becomes a vertical line because the inequality depends only on x. The shading appears to the left or right, depending on the sign and coefficient direction.
5. What happens if A equals zero?
The boundary becomes a horizontal line because the inequality depends only on y. The region shades above or below the line according to the selected relation.
6. Why use a test point?
A test point confirms which side of the boundary satisfies the inequality. It is especially helpful when rearranging signs or checking a graph by hand.
7. Can I use decimals and negative values?
Yes. The calculator accepts decimals, fractions written as decimals, and negative values. That makes it useful for classroom work, homework checks, and custom graph windows.
8. What does the solved form tell me?
The solved form rewrites the inequality into y or x form when possible. This helps identify whether the solution lies above, below, left, or right of the boundary.