About the Direct Variation Calculator

Direct variation describes proportional relationships: y = kx with a constant k. The signature test is a constant ratio — y₁/x₁ must equal y₂/x₂. In practice, find k from any known pair, then scale: if 4 items cost $12 (k = 3), 7 items cost $21.

Proportional Thinking

Direct variation is the mathematical core of unit rates, exchange rates, speed, density, and scaling recipes. Its graph is always a straight line through the origin — no constant term, because at x = 0, y must be 0.