DeltaY

Deltay, typically written as Δy, is a mathematical notation used to denote the change in the y-coordinate between two points in a Cartesian coordinate system. If two points are P1(x1, y1) and P2(x2, y2), then Δy is defined as y2 − y1. In many contexts Δy is paired with Δx, the change in the x-coordinate, to describe the slope of a line, with the slope given by m = Δy/Δx (when Δx ≠ 0). The concept also appears in the description of displacements, where the vertical component of a displacement vector is Δy.

In geometry and physics, the displacement from P1 to P2 is the vector (Δx, Δy), and its length or magnitude is sqrt((Δx)² + (Δy)²). Δy is used to express vertical differences, vertical offsets in graphs, and vertical components in various calculations, including transformations and rendering in computer graphics.

In calculus, Δy contrasts with dy, the latter representing an infinitesimal change in y. For a differentiable function y = f(x), small changes satisfy Δy ≈ f′(x)Δx, and the differential dy is defined as f′(x)dx. Thus Δy is a finite difference, while dy is an infinitesimal or differential form used in integration and differential equations. Delta y is a standard, language-neutral way to describe vertical change across disciplines.