Line Intersection Calculator

Line Intersection Calculator

Find the point where two lines meet, or see when the lines are parallel or the same.

Last updated: June 2026 | By Patchworkr Team

Intersection Solver
Intersection Result
(2, 2)
The lines meet at (2, 2).

What Is the Intersection of Two Lines?

Two non-parallel lines in a plane intersect at exactly one point. If the slopes are equal, the lines are either parallel or the same line, so there is no single intersection point.

How to Solve for the Intersection Point

  1. Enter the slopes and intercepts for both lines.
  2. If the slopes match, check whether the intercepts also match.
  3. If the slopes differ, solve for x using (b2 - b1) / (m1 - m2).
  4. Substitute x back into either equation to get y.
x = (b2 - b1) / (m1 - m2)

Worked Example

For y = x and y = -x + 4, the lines intersect at (2, 2).

x = 2, y = 2

Frequently Asked Questions

What does parallel mean?

Parallel lines have the same slope but different intercepts, so they never meet.

What if the lines are the same?

If both the slope and intercept match, the equations describe the same line and there are infinitely many intersection points.

Does the calculator accept decimals?

Yes. Any finite real slope or intercept is accepted, including scientific notation.

Can the intersection point be fractional?

Yes. The x and y coordinates are often decimals or fractions, so the panel rounds to a readable decimal form.

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