Math

Perpendicular Line Calculator

Find the line perpendicular to y = mx + b through a given point.

Calculated Output

Perpendicular slope -0.5

New y-intercept 3

Formula: Perpendicular slope = −1/m; b = y₀ − (−1/m)·x₀

Step-by-Step Breakdown

1. Values used:

2. Slope of original line = 2

3. Point x = 4

4. Point y = 1

6. Perpendicular slope = -0.5

7. New y-intercept = 3

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The math behind it

If the original slope is m, the perpendicular slope is −1/m. Find the intercept from the point: b = y₀ − (−1/m)·x₀.

Perpendicular to y = 2x through (4, 1) → slope −0.5, y = −0.5x + 3.

What is perpendicular to a horizontal line?

A vertical line, which has an undefined slope.