Find the Domain ax+by=c

Problem

a*x+b*y=c

Solution

1. Identify the type of equation. The equation a*x+b*y=c represents a linear equation in two variables, which graphs as a straight line in the Cartesian plane.

2. Solve for y in terms of x to express the relation as a function, assuming b≠0

b*y=−a*x+c

y=−a/b*x+c/b

3. Analyze the resulting function. Since the expression −a/b*x+c/b is a polynomial of degree 1 (a linear function), there are no square roots of negative numbers, no logarithms of non-positive numbers, and no variables in the denominator.

4. Determine the set of all possible input values for x Because the expression is defined for every real number, the domain is the set of all real numbers.

5. Consider the special case where b=0 If b=0 and a≠0 the equation becomes a*x=c which simplifies to x=c/a This is a vertical line where the domain is restricted to the single value x=c/a However, in the general context of a linear relation y=ƒ(x) we assume the standard functional form.

Final Answer

Domain:(−∞,∞)

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