Math

Intersection of Two Lines Calculator

Find where two lines y = m₁x + b₁ and y = m₂x + b₂ cross.

Calculated Output

x 2

y 5

Formula: x = (b₂ − b₁) ÷ (m₁ − m₂)

Step-by-Step Breakdown

1. Values used:

2. Slope m₁ = 2

3. Intercept b₁ = 1

4. Slope m₂ = -1

5. Intercept b₂ = 7

7. x = Slope m₁ x Intercept b₁ = 2 x 1 = 2

8. y = 5

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The math behind it

Set m₁x + b₁ = m₂x + b₂ and solve: x = (b₂ − b₁) ÷ (m₁ − m₂), then substitute back for y.

y = 2x + 1 and y = −x + 7 → x = 2, y = 5.

What if the slopes are equal?

The lines are parallel and never intersect (or are the same line).