Find the Domain x+3y=-6

Problem

x+3*y=−6

Solution

1. Identify the type of equation. The equation x+3*y=−6 is a linear equation in two variables.

2. Solve for y in terms of x to express the equation as a function.

3*y=−x−6

y=−1/3*x−2

3. Analyze the resulting function ƒ(x)=−1/3*x−2 This is a polynomial function of degree 1.

4. Determine the restrictions. Polynomial functions are defined for all real numbers because there are no denominators containing x that could be zero and no even roots of negative numbers.

5. Conclude that the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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