Definition
Proportional relationship
A relationship where one quantity is always the same multiple of the other.
What it means
The same multiplier links every matching pair. If one quantity doubles or triples, the other does too, and dividing the second quantity by the first always gives the same number.
Remember it
Same multiplier, every pair.
Example
A machine fills 4 bottles each minute. After m minutes it has filled b = 4m bottles, so 1, 2, and 5 minutes match 4, 8, and 20 bottles. The ratio b/m stays 4.
Watch for
A score that starts at 5 points and then gains 3 points each round is linear but not proportional, because it is not 0 when the number of rounds is 0.
Common mix-up
A constant added amount makes a linear pattern; a proportional relationship needs a constant multiplier and a graph through the origin.
Exact meaning
Two quantities have a proportional relationship when one is a constant multiple of the other: y = kx. For x ≠ 0, y/x = k, and the coordinate graph is a straight line through the origin.