Direct proportion
y = kx. Doubling x doubles y. Higher: y ∝ x², y ∝ x³ etc.
If y is directly proportional to x, then y = kx for some constant k. Higher tier extends to y ∝ x&sup{n} for various powers.
Worked examples
y = 5x means y is directly proportional to x with k = 5.
If y = 12 when x = 3, then k = 4 and y = 4x.
Higher: y ∝ x², y = 18 when x = 3 ⇒ k = 2; y = 2x².
Frequently asked questions
How to find k?
Substitute the given pair into y = kx (or y = kx&sup{n} for higher powers) and solve.
Word context?
Cost vs quantity, distance at fixed speed, area ∝ radius² for circles.