Find the Domain 3x+2y=6

Problem

3*x+2*y=6

Solution

1. Identify the type of equation. The equation 3*x+2*y=6 is a linear equation in two variables, which represents a straight line in the Cartesian plane.

2. Solve for y to express the equation in slope-intercept form.

2*y=−3*x+6

y=−3/2*x+3

3. Analyze the resulting function. The expression −3/2*x+3 is a polynomial of degree 1.

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

5. State the domain. The domain of any linear function (that is not a vertical line) is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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