What is the standard form of a linear equation?

The standard form of a linear equation is represented as Ax + By = C. In this format, A, B, and C are integers, and A should not be negative. The purpose of this form is to express a linear relationship between two variables, typically x and y. It allows for easy identification of the slopes and intercepts when rewritten in slope-intercept form, y = mx + b.

This standard form is particularly useful because it can readily accommodate all types of linear equations, including vertical and horizontal lines, which is essential for a comprehensive understanding of linear relationships. By expressing the equation in this way, it's clear how the coefficients A and B relate to the overall graph of the equation in the Cartesian plane.

Other forms presented in the options do not represent the standard form of a linear equation. For instance, y = mx + b is known as the slope-intercept form, which highlights the slope and y-intercept rather than presenting the relationship in standard terms. Similarly, y = ax² + bx + c represents a quadratic equation, not a linear one, which involves a squared term and is fundamentally different in behavior and graph shape. The equation y = kx represents a special case of a linear equation (specifically passing through