Intersection Of Two Lines Calculator

Intersection of Two Lines

Find the intersection point of two lines written in slope-intercept form.

Last updated: June 2026 | By Patchworkr Team

Line Equations

Line 1 slope is required.

Two lines intersect exactly once when their slopes are different.
Results
Enter two non-parallel lines to find the intersection.

How It Works

We solve the system y = m1x + b1 and y = m2x + b2 by setting the equations equal and solving for x.

Then we substitute x back into either equation to get y. If the slopes match, the lines are either parallel or identical, so there is no unique intersection point.

Formula

x
x = (b2 - b1) / (m1 - m2)
y
y = m1x + b1

Example

For y = 2x + 1 and y = -x + 5, the intersection is where 2x + 1 = -x + 5.

3x = 4
x = 4/3
y = 11/3

FAQ

What if the slopes are the same?

If the intercepts are different, the lines are parallel. If they are the same, the lines are identical.

Can the intersection be negative?

Yes. Coordinates can be any real numbers.

Does blank input count as zero?

No. Blank input is treated as missing, not zero.

Why no result for parallel lines?

Because there is no single point where the lines meet.

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