What characterizes a linear equation?

A linear equation is characterized by its ability to represent relationships between variables in a way that produces a straight line when graphed. The option that states it is written in the form ax = b correctly identifies a specific form that a linear equation can take. This format indicates a relationship where 'a' is a constant coefficient, 'x' is the variable, and 'b' is a constant.

While other forms of linear equations, such as y = mx + b, are also common, the essence of a linear equation lies in its linearity—a constant rate of change between variables. This means that irrespective of the form, the equation must exhibit this straight-line relationship, which is accurately captured in the option of being expressed as ax = b, an essential aspect of linear equations in algebra.

The presence of at least one variable is a necessary feature of linear equations, but option C more specifically pinpoints a distinct format that defines linearity in equations. Other forms might introduce curves or other shapes that do not qualify as linear equations, which reinforces the reason why this particular answer is significant in identifying what characterizes a linear equation.