Two Lines Intersection Calculator
y= X +
y= X +
Intersection of two lines
Two Lines Intersection Calculator Overview
This calculator computes the intersection coordinates of two lines (slope-intercept form: y = kx + b), supporting the following features:
- Compute intersection: Input the slopes and intercepts of two lines to automatically calculate their intersection coordinates
- Special case detection: Automatically determine whether the two lines are parallel (no intersection) or coincident (infinite intersections)
Mathematical Formula for Two Lines Intersection
Given the slope-intercept equations of two lines:
Line 1: y = k₁x + b₁
Line 2: y = k₂x + b₂
1. Intersecting Lines (Single Intersection Point)
When k₁ ≠ k₂, the intersection coordinates (x, y) are calculated 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 (Infinite Intersections)
When k₁ = k₂ and b₁ = b₂, the two lines are coincident and have infinitely many intersection points.