Find the Domain x+3y=9

Problem

x+3*y=9

Solution

1. Identify the type of equation. The equation x+3*y=9 is a linear equation in two variables, which represents a straight line in the Cartesian plane.

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

3*y=−x+9

y=−1/3*x+3

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

4. Determine any restrictions on the input x Since there are no denominators containing x no square roots of negative numbers, and no logarithms, the variable x can be any real number.

5. State the domain in interval notation. The domain of all linear functions (that are not vertical lines) is the set of all real numbers.

Final Answer

Domain=(−∞,∞)

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