Parallel and Perpendicular Lines Calculator
Enter the slope and intercept of a line and a point.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Parallel: same slope m, intercept = y₀ − m × x₀
- Perpendicular: slope = −1 ÷ m, intercept = y₀ + x₀ ÷ m
- If m = 0, the perpendicular is x = x₀
To build a line from two points, use the line equation calculator.
Worked example
The line y = 2x + 3 and the point (1, 1):
- Parallel line: y = 2x − 1
- Perpendicular line: y = −0.5x + 1.5
Why your number may differ
Values are rounded to 6 decimal places. A vertical given line has no slope here, so enter it as a two-point line instead.
Frequently asked questions
How do I find a parallel line?
A parallel line has the same slope. Use the point to find its intercept: b = y₀ − m × x₀.
How do I find a perpendicular line?
Its slope is the negative reciprocal, −1 ÷ m. Then find the intercept from the point as before.
What if the slope is 0?
A horizontal line has a vertical perpendicular, written x = a number.