Find the Domain 2x+3y=2

Problem

2*x+3*y=2

Solution

1. Identify the type of equation. This 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 y=ƒ(x)

3*y=−2*x+2

y=−2/3*x+2/3

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

4. Determine the domain. Since there are no values of x that make the expression undefined, the domain consists of all real numbers.

Final Answer

Domain:(−∞,∞)

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