Find the Domain 3x-3y=2

Problem

3*x−3*y=2

Solution

1. Identify the type of equation. The equation 3*x−3*y=2 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. Subtract 3*x from both sides:

−3*y=−3*x+2

3. Divide both sides by −3 to isolate y

y=x−2/3

4. Determine the domain. Since the expression x−2/3 is a polynomial (specifically a linear function), it is defined for all real numbers. There are no denominators containing x that could be zero and no square roots of negative numbers.

5. Express the domain in interval notation. The set of all real numbers is represented as (−∞,∞)

Final Answer

Domain: *(−∞,∞)

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