Parallel and Perpendicular Slopes Explained
How the slopes of parallel and perpendicular lines relate — equal slopes, negative reciprocals, and worked examples.
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Frequently asked questions
What is the slope of a parallel line?
It is the same as the original line’s slope. Parallel lines have equal slopes and differ only in their y‑intercept.
What is the slope of a perpendicular line?
It is the negative reciprocal of the original slope, so the two slopes multiply to −1. Flip the fraction and change the sign — a slope of 2 becomes −1/2.
How do I know if two lines are perpendicular?
Multiply their slopes. If the product is −1, the lines are perpendicular.
Are horizontal and vertical lines perpendicular?
Yes. A horizontal line (slope 0) and a vertical line (undefined slope) meet at a right angle, even though the negative‑reciprocal formula cannot be applied directly.
Parallel and Perpendicular Slopes Explained
Two lines’ slopes instantly tell you whether the lines are parallel, perpendicular, or neither.
Parallel lines
Parallel lines never meet, and they have equal slopes: m₁ = m₂. If one line has a slope of 3, any line parallel to it also has a slope of 3 (only the y‑intercept differs).
Perpendicular lines
Perpendicular lines cross at a right angle, and their slopes are negative reciprocals: m₁ × m₂ = −1. To get a perpendicular slope, flip the fraction and change the sign.
| Original slope | Parallel slope | Perpendicular slope |
|---|---|---|
| 2 | 2 | −1/2 |
| −3 | −3 | 1/3 |
| 1/4 | 1/4 | −4 |
How to find a perpendicular slope
- Write the original slope as a fraction (3 becomes 3/1).
- Flip it (3/1 → 1/3).
- Change the sign (1/3 → −1/3).
A horizontal line (slope 0) and a vertical line (undefined slope) are perpendicular to each other — the one case the reciprocal rule cannot be written as a number.
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