A Line Through the Origin, and the Ratio That Never Moves

You'll learnto recognize a direct proportion y = kx and use the fixed ratio, reporting the value asked.

A direct proportion is y = kx, a line through the origin whose ratio y/x never moves. Points leak in treating an inverse relationship as direct, assuming proportionality where a fixed fee breaks it, and reporting the constant of proportionality instead of the value asked.

8 STEPS · 6 QUICK CHECKS · y = kx through the origin · k is the tool, not the answer · v2

y = kx

Before you start

What you're looking at

A coordinate plane with the line y = 5x rising from the origin, the point (4, 20) marked, beside a direct-proportion card.

The question

What makes a relationship a direct proportion, and what is the ratio that stays fixed?

Watch for

The line climbs from (0, 0); watch that y/x stays 5 at every point — the ratio never moves.

What the symbols mean

In y = kx, k is the constant ratio y/x; a direct proportion is always a line through the origin.

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