The standard form of a line in the Cartesian plane is given by a x + b y = c for real numbers a, b, c element R. This form can be derived from any of the other forms (point-slope form, slope-intercept form, etc.), but can be seen most intuitively when starting from intercept form. Indeed, the intercept form of a line with x-intercept b and y-intercept a is given by x/b + y/a = 1, and so by clearing denominators and setting c = a b, one gets precisely that a x + b y = c.

intercept form | line | linear equation | point-slope form | slope-intercept form | two-point form