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.
Comparing linear and 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.
A linear equation graphs as a straight line; a nonlinear equation, like y = x², graphs as a curve.
Spotting a nonlinear equation
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.