Proportionales

Proportionales refers to the property of two quantities in which one quantity changes in a constant ratio to the other. In mathematics, two variables y and x are directly proportional if there exists a nonzero constant k such that y = kx. The constant k is called the proportionality constant or constant of proportionality.

Directly proportional relationships have several characteristic features: the graph of y versus x is a straight line that passes through the origin, and the ratio y/x remains constant for all valid pairs (x, y). Inverse proportionality describes a different kind of relationship, where y is proportional to the reciprocal of x, written as y = k/x, or equivalently yx = k remains constant. Both direct and inverse proportionalities express a consistent relationship between the quantities, but they behave differently as x changes.

Common ways to identify proportional relationships include examining ratios and products: for direct proportionality, y/x should be constant; for inverse proportionality, yx should be constant. A proportional relationship differs from a linear relationship with a nonzero intercept; if y = kx + b with b ≠ 0, the relation is not proportional.

Applications of proportionality span sciences and everyday problems. Examples include cost being proportional to quantity times unit price, area scaling with the square of a linear dimension in similar figures, and physical laws that relate variables with constant factors, such as speed, concentration, or intensity under ideal conditions. Proportional reasoning is a foundational skill in mathematics education and is used to model and analyze real-world relationships.