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

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

This calculator takes two coordinate points (x1, y1) and (x2, y2) and computes the full linear equation in slope-intercept form (y = mx + b). It also calculates the slope, y-intercept, x-intercept, and the straight-line distance between the two points. A live SVG graph updates as you type so you can visualize the line immediately.

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

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