Two Lines Intersection Calculator

About the Two Lines Intersection Calculator

This calculator computes the intersection point of two lines given in slope-intercept form (y = kx + b). It supports the following:

• Intersection point: enter the slopes and intercepts of the two lines to compute the intersection coordinates automatically.
• Special case detection: automatically determines whether the two lines are parallel (no intersection) or coincident (infinitely many intersections).

Math Behind the Intersection of Two Lines

Given the two lines in slope-intercept form: line 1: y = k₁x + b₁, line 2: y = k₂x + b₂.

• 1. Intersecting lines (a unique intersection): when k₁ ≠ k₂, the intersection (x, y) is computed as: x = (b₂ - b₁)/(k₁ - k₂), y = k₁x + b₁.
• 2. Parallel lines (no intersection): when k₁ = k₂ and b₁ ≠ b₂, the two lines are parallel and have no intersection.
• 3. Coincident lines (infinitely many intersections): when k₁ = k₂ and b₁ = b₂, the two lines are coincident and have infinitely many intersections.