Graph of y = x
Interactive graph of y = x (identity function / linear). Explore the simplest linear function, its slope, and role as a reference line.
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Drag to pan, scroll to zoom, click on the curve to pin coordinates. Edit equations in the sidebar.
Understanding the Function
The function y = x is the identity function and the simplest linear equation. Its graph is a straight line passing through the origin at a 45-degree angle, with a slope of exactly 1. Every point on the line has equal x and y coordinates.
The identity line y = x serves as a fundamental reference in mathematics. It is the mirror line for finding inverse functions: if you reflect the graph of any function across y = x, you get its inverse. It also represents perfect correlation in statistics, perfect prediction in machine learning, and proportional response in linear systems.
Key properties: slope of 1, y-intercept at 0, passes through the origin, domain and range are both all real numbers. It is both an odd function (f(-x) = -f(x)) and the only function that is simultaneously linear, passes through the origin, and has a slope of 1. The derivative is 1 everywhere.