What distinguishes a non-linear equation?

A non-linear equation is primarily characterized by the presence of variables that are raised to a power other than one or by the multiplication of variables together. This distinguishes it from linear equations, which only contain variables raised to the first power and do not involve products of variables. In a non-linear context, the relationships described by the equation can be quadratic, cubic, exponential, or of other forms that introduce curvature or non-constant rates of change in their graphs.

For example, an equation like (y = x^2) is non-linear because the variable (x) is raised to the second power. Similarly, equations such as (y = x^3 + 2x) or (y = x \cdot z), where variables are multiplied together, illustrate non-linearity.

The other options address characteristics that do not define non-linearity. For instance, having constant coefficients indicates a linear equation, while involving only one variable does not necessarily imply that the equation is non-linear. Lastly, merely stating that an equation is linear does not provide any distinguishing features of non-linear equations. Therefore, the correct characterization that encompasses the defining traits of a non-linear equation is the raising of variables to non-first powers or their multiplication