In what form is the equation of a line written as Ax + By = C?

The equation of a line written in the form ( Ax + By = C ) is referred to as the standard form of a linear equation. In this format, ( A ), ( B ), and ( C ) are integers, and ( A ) should be non-negative. The standard form is useful for various applications, such as finding intercepts or rewriting the equation into different forms, including slope-intercept form.

In contrast, the slope-intercept form expresses the line as ( y = mx + b), where ( m ) represents the slope and ( b ) represents the y-intercept. Point-slope form is written as ( y - y_1 = m(x - x_1) ), which is useful when you know a point on the line and the slope. Function notation simply indicates a function, typically denoted as ( f(x)) or similar, but does not specifically relate to the standard representation of a line.

This understanding of the standard form is crucial for solving problems involving linear equations and provides a clear structure for analyzing linear relationships.