What is slope-intercept form?

Slope-intercept form is y = mx + b, where m is the slope (rise over run) and b is the y-intercept (the y value when x = 0). It is the most common way to express a linear equation.

What happens if the two points have the same x coordinate?

If x1 equals x2, the line is vertical (undefined slope). The calculator detects this and reports it as a vertical line with the equation x = x1 rather than crashing.

What if the two points are identical?

If both points are the same, a unique line cannot be defined. The calculator shows an inline error asking you to enter two distinct points.

How is the distance calculated?

Distance uses the Euclidean formula: sqrt((x2 - x1)^2 + (y2 - y1)^2), which is the straight-line distance between the two points.

Can I use decimal or negative coordinates?

Yes. The calculator accepts any real number including decimals and negatives for all four coordinate fields.

Line Equation from Two Points

Name: Line Equation from Two Points
Availability: InStock
Author: Nham Vu

Enter two coordinate points and instantly get the slope-intercept equation, intercepts, and distance with a live graph.

Enter Two Points

Point 1

x₁

y₁

Point 2

x₂

y₂

Graph

Enter two points to see the graph

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Summary

Enter two coordinate points and instantly get the slope-intercept equation, intercepts, and distance with a live graph.

How it works

Enter the x and y coordinates for the first point (x1, y1).
Enter the x and y coordinates for the second point (x2, y2).
The slope m is calculated as (y2 - y1) / (x2 - x1).
The y-intercept b is derived from y = mx + b using one of the points.
The x-intercept is found by solving 0 = mx + b for x.
Distance is computed using the Pythagorean theorem: sqrt((x2-x1)^2 + (y2-y1)^2).

Use cases

Verify homework answers for linear equation problems.
Find the equation of a trend line through two data points.
Calculate slope and intercepts for engineering or design problems.
Visualize how changing coordinates shifts the line on a graph.
Determine the distance between two locations on a coordinate map.
Check if three points are collinear by testing the same equation.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu