Direct and inverse proportion
Direct: y ∝ x (y = kx). Inverse: y ∝ 1/x (y = k/x).
Direct proportion: as one quantity grows, the other grows in the same ratio (cost ∝ quantity). Inverse: one grows as the other shrinks (speed ∝ 1/time for a fixed distance).
Worked examples
Direct: 3 books cost £12, so 5 books cost £20. £4 each.
Inverse: 4 painters take 6 days; 8 painters take 3 days. Workers×days = 24.
y = 5x means y is directly proportional to x with constant 5.
Frequently asked questions
How do I spot which?
Direct: doubling x doubles y. Inverse: doubling x halves y. The product xy stays constant for inverse.
Algebraic notation ∝?
‘y ∝ x’ means ‘y is proportional to x’. To use it, replace with y = kx and find k from given values.