What is the standard form of a linear equation?

The standard form of a linear equation is represented as Ax + By = C, where A, B, and C are constants. In this format:

• A and B are the coefficients of the variables x and y, respectively, and they cannot both be zero.

• C is a constant that represents the value at which the linear relationship is equal to.

This form is particularly useful because it clearly shows the relationship between the two variables in a way that highlights their coefficients and the constant term, making it easier to analyze the equation for various purposes, such as graphing or solving for one variable in terms of the other.

The other options represent different types of equations. For example, y = mx + b is the slope-intercept form of a linear equation, which emphasizes the slope and y-intercept rather than the coefficients in the standard form. y = Ax^2 + Bx + C represents a quadratic equation and indicates a parabolic relationship, which is fundamentally different from a linear relationship. Lastly, x^2 + y^2 = r^2 is the equation of a circle, illustrating a non-linear relationship between x and y. Therefore, the correct representation of a linear equation in standard form is Ax + By = C.