Direct Variation

Apples cost the same per kilo. 5 kilos cost 15 dollars and 10 kilos cost 30. Double the weight and the price doubles: the price varies directly with the weight.

In symbols, $y = kx$, where k is a fixed number called the constant of variation. To find it, divide one y by its x: $k = \frac{15}{5}$, which is 3. So the rule is $y = 3x$, 3 dollars a kilo, and 7 kilos cost 21 dollars.

The ratio $\frac{y}{x}$ is the same for every pair, which is how you spot direct variation in a table. Its graph is a line through (0, 0) with slope k: no apples cost nothing.