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 constants, and ( x ) and ( y ) are variables. This format is particularly useful for quickly identifying the coefficients of ( x ) and ( y ), as well as the constant term, allowing for straightforward analysis of the equation's properties.

Standard form is advantageous because it allows for easy manipulation and is the preferred form when working with systems of linear equations, especially in the context of graphing or finding intercepts. In addition, having ( a ) and ( b ) as integers (and ideally positive) simplifies the process of identifying the slope and y-intercept, as well as applying techniques like elimination in systems of equations.

The other options represent different forms of linear equations. The first option ( y = mx + b ) is known as slope-intercept form, which is useful for directly identifying the slope and y-intercept. The third option ( y - y_1 = m(x - x_1) ) is point-slope form, typically used when you know the slope and a particular point on the line.