proportionale

Proportionale is the Italian term used in mathematics and related disciplines to describe a proportional relationship between two quantities. When one quantity depends directly on another, they are proportional: there exists a constant k such that y = kx. The constant k is called the coefficient or constant of proportionality; it sets the scale of the relationship. Graphically, a directly proportional pair yields a straight line through the origin with slope k. If x doubles, y doubles; if x increases by a certain percentage, y changes by the same percentage.

The opposite case, inverse proportionality, occurs when y is proportional to 1/x, written as y = k/x, and produces a hyperbola. In Italian usage, one distinguishes proporzionale diretta (direct proportionality) and proporzionale inversa (inverse proportionality). In applied contexts, proportional relations appear in physics (for example, F ∝ x in Hooke’s law), chemistry (concentrations and reaction rates under certain conditions), and economics (cost proportional to quantity). They provide a simple model for scaling and unit-consistent predictions.

In education, problems commonly ask to identify whether quantities are proportional, determine k from given pairs, and apply proportional reasoning to new values. The term also appears in phrases such as coefficiente di proporzionalità and legge di proporzionalità, reflecting the central role of proportionality in quantitative reasoning.