Direct Proportion

Two quantities are in direct proportion when doubling one doubles the other — halve one and the other halves too. They always keep step, linked by a single multiplier:

y = kx

The number k is the constant of proportionality: the fixed amount of y for every one unit of x.

The cleanest way to use a proportion is the unitary method: find the value of one, then multiply. If 3 pens cost £1.20, then one pen costs 1.20 \div 3 = 0.40 (40p), so 5 pens cost 0.40 \times 5 = 2.00 (£2.00).

When y is directly proportional to x:

they are linked by y = kx;
the graph is a straight line through the origin with gradient k;
find k = y \div x from one matching pair, then use it for any other;
the unitary method is the same idea — find the value of one unit first, then scale up.

Drive the line yourself

Pull the slider to change the constant k. The line always passes through the origin — a bigger k just tilts it steeper.