Find the Domain -3x=6y-2

Problem

−3*x=6*y−2

Solution

1. Identify the type of equation. The equation −3*x=6*y−2 is a linear equation in two variables.

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

6*y=−3*x+2

y=(−3*x+2)/6

y=−1/2*x+1/3

3. Analyze the resulting function. The expression −1/2*x+1/3 is a polynomial (specifically a linear function).

4. Determine the constraints. Polynomials 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. State the domain in interval notation. Since there are no restrictions on x the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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