Calculator inputs
Choose an input mode, enter the known values, and generate the line in several equivalent forms.
Example data table
| Mode | Input values | Generated equation | Slope |
|---|---|---|---|
| Two points | (1, 2) and (5, 10) | y = 2x | 2 |
| Point and slope | (3, 4), m = -1 | y = -x + 7 | -1 |
| Intercepts | x = 4, y = 6 | 3x + 2y = 12 | -1.5 |
| Coefficients | 2x - y + 3 = 0 | y = 2x + 3 | 2 |
Formula used
Two-point form: When two points are known, slope is m = (y₂ - y₁) / (x₂ - x₁).
Point-slope form: A line through (x₁, y₁) with slope m is y - y₁ = m(x - x₁).
Slope-intercept form: When slope and y-intercept are known, use y = mx + b.
Intercept form: When x- and y-intercepts are known, use x/a + y/b = 1.
General form: Every generated line is also expressed as Ax + By + C = 0, then simplified to integer coefficients.
The calculator also derives angle, rise-over-run, distance from the origin, and sample points using the generated equation.
Vertical lines are handled separately because their slope is undefined and their equation becomes x = constant.
How to use this calculator
Start by selecting the generation mode that matches the information you already know. Each mode reveals only the fields needed for that method.
Enter numeric values for the visible inputs. You can also set decimal precision and provide custom x-values for the output point table.
Press Generate line equation. The result panel appears below the header and above the form, showing the line in multiple forms.
Use the export buttons to save the summary as CSV or PDF for classes, worksheets, notes, or quick reference.
FAQs
1. What does this calculator generate?
It builds a line equation from different input styles, then converts that line into slope-intercept, point-slope, standard, general, and intercept forms whenever possible.
2. Can it solve vertical lines?
Yes. Vertical lines are detected automatically. Instead of forcing a slope-intercept result, the calculator reports the correct equation as x equals a constant.
3. Why is the slope sometimes undefined?
Slope is undefined when the run is zero. That happens for vertical lines because x stays constant while y changes.
4. What is the benefit of multiple forms?
Different math tasks prefer different forms. Graphing often uses slope-intercept, proof work may use general form, and geometry problems often start from two points.
5. Does the calculator simplify coefficients?
Yes. The general equation is normalized to reduced integer coefficients when possible, making the standard and general forms easier to read and compare.
6. What are sample points used for?
Sample points help verify the line quickly. They also make graph plotting easier because you can test several coordinates from one generated equation.
7. Can I enter decimal values?
Yes. Decimals are supported across all modes. The calculator rounds displayed answers to your selected precision while keeping the internal math consistent.
8. What does distance from origin mean?
It is the shortest perpendicular distance between the generated line and the origin point. This value comes directly from the general line equation.