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Introduction to nonlinear equations

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Nonlinear Equations

A linear equation graphs as a straight line and can be written as y = mx + b. A nonlinear equation is any equation whose graph is a curve rather than a straight line, such as y equals x squared. Learn how to tell linear and nonlinear equations apart.

What a nonlinear equation is

A linear equation graphs as a straight line and can be written in the form y = mx + b. A nonlinear equation is any equation whose graph is not a straight line — a curve, instead of a line, means the equation is nonlinear.

The equation y = x + 1 is linear: every point rises at the same constant rate, producing a straight line. The equation y = x² is nonlinear: as x grows, y grows faster and faster, curving the graph into a parabola.

Linear vs. nonlinear equations On the left, the linear equation y = x + 1 graphs as a straight line. On the right, the nonlinear equation y = x squared graphs as a curved parabola, since its graph is not a straight line. Linear: y = x + 1 Nonlinear: y = x²
A linear equation graphs as a straight line; a nonlinear equation, like y = x², graphs as a curve.

An equation is nonlinear if a variable is raised to a power other than 1, multiplied by another variable, or placed inside a root or denominator. Recognizing this distinction matters before you try to graph using a table of values or a slope, since those straight-line methods only apply to linear equations. It builds on tables of values for linear relations and on being comfortable with identifying functions in the first place.

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