Linearly

Linearly is an adverb derived from the adjective linear. It denotes actions, relationships, or phenomena that follow the principles of linearity: proportional change, additive effects, and adherence to a straight-line relation between variables. Describing a relationship as linear or growing linearly conveys that the outcome changes at a constant rate with respect to the input, within the scope of the model or measurement.

In mathematics, "linearly" is used to qualify equations, transformations, and relationships that respect linearity. A linear equation in two variables has the form y = ax + b. A transformation T is linear if T(a v + b w) = a T(v) + b T(w). A set of vectors is linearly independent if no vector can be expressed as a linear combination of the others; otherwise they are linearly dependent.

Linearly linked concepts also appear in physics and computer science. A linearly proportional relationship means one quantity changes in direct proportion to another. In computing, linear time algorithms run in time proportional to the input size, and systems described as linearly scalable maintain proportional performance as resources grow. In statistics and data analysis, linearly related variables lie on or near a straight line when plotted.

Origin: from Latin linearis "of a line" and linea "line".