Proportjonal

Proportional is an adjective used in mathematics, physics, and related disciplines to describe a relationship in which one quantity scales in a constant ratio to another. In its most common form, two variables x and y are directly proportional if there exists a nonzero constant k such that y = kx for all values in the domain. In this case, increasing x causes a proportional increase in y, and the ratio y/x remains constant at k. When y is inversely proportional to x, there exists k such that y = k/x, so increasing x causes y to decrease accordingly.

Proportional relationships are graphically represented by a straight line through the origin with slope k. They differ from general linear relationships that may have a nonzero intercept (y = mx + b with b ≠ 0).

Applications of proportionality appear across disciplines. In physics, many quantities are proportional to one another under fixed conditions: voltage is proportional to current when resistance is constant, and electrical power is proportional to the square of the current, P = I^2R. In control theory, proportional control uses an output proportional to the measurement error, typically written as output = Kp × error. In political science, proportional representation allocates seats in proportion to the shares of votes received.

Etymology and usage: the term derives from Latin proportionem, meaning a ratio or relation. Across languages, proportional concepts appear in mathematics, science, and governance to describe scaling relationships.