Find the Domain 2x+3y=6

Problem

2*x+3*y=6

Solution

1. Identify the type of equation. The equation 2*x+3*y=6 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=−2*x+6

y=−2/3*x+2

3. Analyze the resulting function ƒ(x)=−2/3*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 values, and no logarithms, the variable x can take any real value.

5. State the domain in interval notation. The domain of any non-vertical linear function is the set of all real numbers.

Final Answer

Domain:(−∞,∞)

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