Find the Domain 2x+6y=12

Problem

2*x+6*y=12

Solution

1. Identify the type of equation. The given equation 2*x+6*y=12 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.

6*y=−2*x+12

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. Since there are no denominators containing x no square roots of negative numbers, and no logarithms, the variable x can take any real value.

5. State the domain in interval notation. The set of all possible input values for x is all real numbers.

Final Answer

Domain: *(−∞,∞)

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