What is the standard form of a linear equation?

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are integers. This format offers several key benefits for understanding and working with linear equations. First, it allows for easy interpretation of the coefficients A and B, which represent the slopes and intercepts of the line when manipulated into slope-intercept form (y = mx + b). In standard form, it is also straightforward to identify the intercepts and to rearrange the equation for graphing.

Additionally, the requirement that A and B are integers ensures that the equation of the line is consistent and manageable within the context of integer solutions and applications, especially relevant in business and social science mathematical modeling.

In contrast, other forms like y = mx + b highlight the slope and y-intercept more directly, yet do not conform to the standard form designation. The equation y = ax² + bx + c represents a quadratic function rather than a linear equation, and x + y + z = D involves multiple variables, which also does not fit the criteria for a linear equation in standard form.