Find the Domain 2x+8y=-6

Problem

2*x+8*y=−6

Solution

1. Identify the type of equation. The equation 2*x+8*y=−6 is a linear equation in two variables.

2. Solve for y to express the equation as a function of x Subtract 2*x from both sides.

8*y=−2*x−6

3. Divide both sides by 8 to isolate y

y=(−2*x−6)/8

4. Simplify the fraction.

y=−1/4*x−3/4

5. Determine the domain. Since the resulting expression is a linear polynomial, there are no values of x that cause division by zero or involve square roots of negative numbers.

6. Conclude that the function is defined for all real numbers.

Final Answer

Domain: *(−∞,∞)

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