Algebra
Direct & inverse proportion
Twice the input, twice (or half) the output — two flavours of proportion.
Direct: y goes up as x goes up. Inverse: y goes down as x goes up.
Try this
4
y = k/x ⇒ x·y stays constant at 12 = x = 4 ⇒ y = 12/4 = 3 (x·y = 12)
Spot the relationship
- Direct: y = kx — double x, double y; the ratio y/x is fixed.
- Inverse: y = k/x — double x, halve y; the product xy is fixed.
- Find k from one known pair, then use it for any other value.
Your turn
y is inversely proportional to x, and y = 6 when x = 4. Find y when x = 8.
Fixed distance: speed × time = distance. As speed rises, time falls — a classic inverse relationship.
Two forms
- Direct: y = kx (constant ratio).
- Inverse: y = k/x (constant product).
Try it
Speed × time = distance. Fixed distance — what kind of relationship?
Inverse: as speed goes up, time goes down.