How do two lines intersect?
Set the expressions equal and solve for x, then y.
Point of Intersection Calculator
Solve for the intersection of two non-vertical lines in slope-intercept form.
Enter two line equations
Provide slopes m1, m2 and intercepts b1, b2.
About this calculator
How to use Point of Intersection Calculator, plus the formulas and logic behind the results.
Tool description
At an intersection the y-values match: m1x + b1 = m2x + b2. Solving gives x, then y.
How to use
- Enter slope and intercept for line 1.
- Enter slope and intercept for line 2.
- Select Calculate.
- Read the intersection point or a parallel/coincident message.
Formulas & reference
m1 x + b1 = m2 x + b2x = (b2 − b1) / (m1 − m2)y = m1 x + b1
Line cases
- Different slopes → one point
- Same slope, different b → none
- Same slope and b → infinitely many
- Example: y=2x+1 and y=−x+4 meet at (1,3)
Calculation logic
If slopes differ, computes unique intersection. Equal slopes with different intercepts are parallel; equal slopes and intercepts are coincident.
Vertical lines are not representable as y = mx + b.
Point of Intersection Calculator FAQ
Common questions about this calculator and how to use the results.
What if slopes are equal?
The lines are parallel (no intersection) or the same line.
Can intersection be off-axis?
Yes—any real point is possible.
Are vertical lines supported?
Not in slope-intercept form; use a different equation form.
Do I need graphs?
No—the algebra alone finds the point.
What if denominators are tiny?
Nearly parallel lines produce very large |x|; results may be sensitive.