Skill: parallel-perpendicular

Parallel & Perpendicular Tutor Help

Stuck on parallel & perpendicular? Review the core ideas, read answers to common questions, and send a question to a tutor.

1 Quick recap

Parallel lines share a slope; perpendicular slopes are opposite reciprocals — flip the fraction and change the sign, so their product is −1. To write one through a point, take the new slope and plug the point into y = mx + b.

Core ideas

Parallel: m1 = m2. Perpendicular: m1 · m2 = −1.
Opposite reciprocal: flip and change sign (2/3 ↔ −3/2).
New line through (x1, y1): b = y1 − m_new · x1.
Horizontal (m = 0) is perpendicular to vertical (undefined).
Same slope + same intercept = the same line, not just parallel.

2 Questions students ask

The questions a tutor hears most about this skill.

How do I remember which is which?

Parallel = “pair-allel”: the slopes pair up equally. Perpendicular = “product −1”: flip and negate. If you only flip (2/3 → 3/2), you missed the sign — both moves, every time.

Can two lines with the same slope still intersect?

Only if they are the same line (same intercept too). Distinct parallel lines never meet; coincident lines meet everywhere.

What is the perpendicular to a vertical line?

A horizontal line (slope 0). The flip-and-negate rule needs a slope to start from; vertical lines have none, so handle them as the special case.

3 Ask a tutor

Stuck on a problem? Send it in — a tutor will walk you through it.

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