Definition
Direct proportion
When one quantity is scaled, the other is scaled by exactly the same factor.
What it means
Think of a recipe that never changes. If one batch needs 3 cups of water, two batches need 6 and four batches need 12. The number of batches and the water amount grow together by the same scale factor.
Remember it
Same-factor partners: scale one quantity, and the other scales the same way.
Example
A machine uses 2 metres of ribbon for 5 badges. Fifteen badges is 3 times as many, so the ribbon amount is also 3 times as much: 2 × 3 = 6 metres.
Watch for
Both quantities increasing is not enough. In direct proportion, they must change by matching multiplication factors, and the graph passes through the origin.
Common mix-up
Adding the same amount to both quantities does not preserve direct proportion; matching factors, not matching additions, are what matter.
Exact meaning
Two quantities are in direct proportion when y = kx for a constant k. For every nonzero x, the ratio y/x is the same; multiplying x by a factor multiplies y by that same factor.