Find the Domain 2x-6y=8

Problem

2*x−6*y=8

Solution

1. Identify the type of equation. The equation 2*x−6*y=8 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.

−6*y=−2*x+8

3. Divide both sides by −6 to isolate y

y=(−2*x+8)/(−6)

4. Simplify the expression.

y=1/3*x−4/3

5. Determine the domain. Since the resulting function is a polynomial (specifically a linear function), there are no values of x that result in division by zero or the square root of a negative number. Therefore, x can be any real number.

Final Answer

Domain: *(−∞,∞)

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