Point-Slope Form Calculator - Free

Enter Your Values

Input Mode

x₁

y₁

x₂

y₂

Results & Breakdown

Point-Slope Form

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Slope (m)

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Slope (Decimal)

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Slope Angle

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y-Intercept

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Point Used

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Substituted formula:

How to Use This Calculator

Choose Two Points to calculate slope from two coordinate pairs, or Point & Slope if you already know the slope.
Enter your values. You can use integers, decimals, or fractions like 3/4.
Click Calculate to see the point-slope equation, slope, intercept, and graph.
Use the Reset button to start over with default values.

Calculation Method & Data

The point-slope form of a linear equation is:

y − y₁ = m(x − x₁)

Where m is the slope and (x₁, y₁) is a point on the line.

When given two points (x₁, y₁) and (x₂, y₂), the slope is calculated as:

m = (y₂ − y₁) / (x₂ − x₁)

Edge cases handled:

Vertical line (x₁ = x₂): slope is undefined; equation is x = x₁.
Horizontal line (y₁ = y₂): slope is 0; equation is y = y₁.
Identical points: no unique line (infinite solutions).
Fraction inputs are supported (e.g., 3/4, -2/5).
Results include both exact fraction and decimal forms.

Worked Point Slope Form Example

Example: Find the point-slope form of the line passing through (2, 3) and (6, 11).

Step 1 — Find the slope:
m = (11 − 3) / (6 − 2) = 8 / 4 = 2

Step 2 — Use point-slope form with (2, 3):
y − 3 = 2(x − 2)

Step 3 — Verify: Substitute x = 6: y − 3 = 2(6 − 2) = 8 → y = 11 ✓

Result: y − 3 = 2(x − 2) or equivalently y = 2x − 1.

How to Interpret the Results

Point-Slope Form: The equation written as y − y₁ = m(x − x₁).
Slope (m): The steepness of the line. Positive = rising, negative = falling, zero = horizontal, undefined = vertical.
Slope Angle: The angle the line makes with the positive x-axis, in degrees (arctan of the slope).
y-Intercept: Where the line crosses the y-axis (value of y when x = 0).
Point Used: The (x₁, y₁) coordinate used in the point-slope equation.
Graph: A visual plot of the line with the point(s) and intercepts highlighted.

Assumptions and Limits

This calculator works for linear equations in two variables.
Input values are treated as real numbers; complex numbers are not supported.
Fractions must use a forward slash (e.g., 3/4); mixed numbers like 1 1/2 are not supported — use 1.5 or 3/2.
When two identical points are entered, the calculator reports an infinite number of solutions (any line through that point).
For vertical lines, the slope is undefined and the equation is reported as x = constant.
Graph is rendered on a fixed aspect ratio; extreme values may compress the visible range.
Results are rounded to 6 decimal places for display; exact fractions are provided where applicable.

Frequently Asked Questions

What is point-slope form?

Point-slope form is a way to write the equation of a straight line using its slope and one point on the line: y − y₁ = m(x − x₁).

How do I find point-slope form from two points?

First calculate the slope m = (y₂ − y₁) / (x₂ − x₁), then substitute m and either point into y − y₁ = m(x − x₁).

Can I enter fractions like 3/4?

Yes. The calculator accepts fractions in the form a/b (e.g., 3/4, -2/5) and decimals.

What happens if the two points are the same?

If both points are identical, there is no unique line through them — infinitely many lines pass through a single point. The calculator will report this case.

How do you handle a vertical line?

A vertical line occurs when x₁ = x₂. The slope is undefined, and the equation is written as x = x₁. The calculator handles this edge case.

Is the slope the same as the angle?

No. The slope is the ratio of rise over run. The slope angle is the angle the line makes with the positive x-axis, calculated as arctan(m) in degrees. They are related but different.

Does the calculator show a graph?

Yes. When a valid linear equation is calculated, an interactive graph of the line is displayed, along with the relevant points and intercepts.

Point Slope Form Calculator