Calculated Result
Rounded values are shown to six decimal places when needed.
Generated Coordinate Table
| # | x | y |
|---|
Plotly Graph
Interactive line viewCalculator Inputs
Use decimals or fractions such as 3/4, -5/2, or 0.125.
Example Data Table
| Mode | Inputs | Point-Slope Form | Slope-Intercept Form | Standard Form |
|---|---|---|---|---|
| Point and slope | (x₁, y₁) = (2, 5), m = 3 | y - 5 = 3(x - 2) | y = 3x - 1 | 3x - y - 1 = 0 |
| Point and slope | (x₁, y₁) = (-1, 4), m = -2 | y - 4 = -2(x + 1) | y = -2x + 2 | 2x + y - 2 = 0 |
| Two points | (1, 2) and (5, 10) | y - 2 = 2(x - 1) | y = 2x | 2x - y = 0 |
Formula Used
The main equation for this tool is the point-slope form of a straight line:
y - y₁ = m(x - x₁)
Here, m is the slope and (x₁, y₁) is a known point on the line.
When needed, the calculator converts the result into slope-intercept form:
y = mx + b, where b = y₁ - mx₁
It also builds standard form as:
Ax + By + C = 0
If you use two points, the slope is first calculated with:
m = (y₂ - y₁) / (x₂ - x₁)
For a vertical line, the slope is undefined and the equation is written as x = constant.
How to Use This Calculator
Step 1: Choose either Point and slope or Two points.
Step 2: Enter the known coordinates. If you chose the first mode, also enter the slope.
Step 3: Optionally enter an x-value to evaluate y, plus graph limits for the interactive chart.
Step 4: Click Calculate. The result appears above the form and below the header.
Step 5: Review the point-slope form, slope-intercept form, standard form, intercepts, coordinate table, and graph.
Step 6: Use the export buttons to download a CSV file or a PDF report.
FAQs
1) What is point-slope form?
Point-slope form uses one known point and the slope. It is often the fastest way to write a line equation when those values are already given.
2) Can I enter fractions instead of decimals?
Yes. Enter values like 3/4, -5/2, or 0.125. The calculator converts valid fractions and decimals into numeric results automatically.
3) Can this calculator work from two points?
Yes. Switch to Two Points mode, enter both coordinates, and the tool calculates the slope before building the line equation.
4) What happens with a vertical line?
Vertical lines have undefined slope, so slope-intercept form does not exist. The calculator shows the correct equation as x = constant instead.
5) Why does the calculator show standard form too?
Standard form is useful for algebraic manipulation, comparison, and some graphing tasks. Slope-intercept form is often easier for reading slope and intercepts.
6) What do the CSV and PDF exports include?
The CSV file stores the result summary and generated coordinate table. The PDF version creates a printable report with equations and key values.
7) Can I evaluate the line at a specific x-value?
Yes. Enter any x-value and the calculator evaluates the matching y-value, unless the line is vertical and does not define one y for each x.
8) Why is the graph useful?
The graph confirms the point location, line direction, intercept behavior, and steepness. It helps you verify whether the equation matches your expectations.