Line Intersection Calculator
Set the two equations equal and solve. The difference of the intercepts over the difference of the slopes gives x; feeding that x back into either line gives y.
Your numbers
x
4
y
6
Angle (°)
71.57°
Formula
x = (Second y-intercept − y-intercept) ÷ (Slope − Second slope)
Equal slopes mean parallel lines that never cross, and the result shows as zero.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| SlopeHow much y rises per 1 of x — the m in y = mx + b. | 1 | No limit |
| y-interceptWhere the line crosses the y axis — the b in y = mx + b. | 2 | No limit |
| Second slopeThe second line’s slope; equal slopes are parallel and never meet. | -0.5 | No limit |
| Second y-interceptWhere the second line crosses the y axis. | 8 | No limit |
Step by step
Quick reference table
Results when only y-intercept changes and everything else stays put.
| y-intercept | x | y | Angle (°) (°) |
|---|---|---|---|
| 1 | 4.6667 | 5.6667 | 71.57 |
| 1.5 | 4.3333 | 5.8333 | 71.57 |
| 2 | 4 | 6 | 71.57 |
| 3 | 3.3333 | 6.3333 | 71.57 |
| 4 | 2.6667 | 6.6667 | 71.57 |
What each result means
| Result | At default values |
|---|---|
| xThe horizontal position in Cartesian form. | 4 |
| yThe vertical position in Cartesian form. | 6 |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 71.57 |
Common mistakes
Equal slopes mean parallel lines that never cross, and the result shows as zero.
Glossary
- Slope
- How much y rises per 1 of x — the m in y = mx + b.
- y-intercept
- Where the line crosses the y axis — the b in y = mx + b.
- Second slope
- The second line’s slope; equal slopes are parallel and never meet.
- Second y-intercept
- Where the second line crosses the y axis.
- x
- The horizontal position in Cartesian form.
- y
- The vertical position in Cartesian form.
- Angle (°)
- An angle in degrees; a full turn is 360°.
Frequently asked questions
Q. How is Line Intersection Calculator calculated?
x = (Second y-intercept − y-intercept) ÷ (Slope − Second slope) — Set the two equations equal and solve. The difference of the intercepts over the difference of the slopes gives x; feeding that x back into either line gives y.
Q. Can you walk through an example?
With Slope 1, y-intercept 2, Second slope -0.5, Second y-intercept 8, the answer is x 4.
Q. What do I need to enter?
Enter Slope, y-intercept, Second slope, Second y-intercept. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only y-intercept moves the answer to y-intercept 1 → x 4.6667 and y-intercept 4 → x 2.6667. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Equal slopes mean parallel lines that never cross, and the result shows as zero.
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Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.