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. Subtract 3*x from both sides.

−2*y=−3*x+6

3. Divide both sides by −2 to isolate y

y=3/2*x−3

4. Determine the domain. In a linear function of the form y=m*x+b there are no square roots of negative numbers, no divisions by zero, and no logarithms of non-positive numbers.

5. Conclude that the input x can be any real number.

Final Answer

Domain: *(−∞,∞)

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