What is the relationship between the coefficients in the standard form ax + by = c?

The correct answer reflects that in the standard form equation ( ax + by = c ), the coefficients ( a ) and ( b ) must indeed be integers. This is primarily a convention in mathematics, particularly when solving linear equations and systems of equations, as using integers can simplify calculations and interpretations without loss of generality.

Having ( a ) and ( b ) as integers ensures that the equation represents a line in the Cartesian plane with easily identifiable slope and intercepts, and it also allows for the potential use of various numerical methods which assume integer coefficients. Furthermore, while the value of ( c ) can also be an integer, it is the coefficients ( a ) and ( b ) that are specifically referred to in this context.

The other options present certain limitations or misinterpretations of the requirements. For example, while it is true that coefficients can be any real numbers mathematically, this does not hold for the standard form which typically necessitates integer values. Additionally, the stipulation that coefficients must be positive integers is too restrictive, as negative integers or zero may fulfill the requirements of the equation and still lead to valid representations of lines. Finally, the notion that the coefficients must be equal is not a requirement for