Find the Domain 2x-8y=5

Problem

2*x−8*y=5

Solution

1. Identify the type of equation. The equation 2*x−8*y=5 is a linear equation in two variables.

2. Solve for y to express the equation as a function of x

8*y=2*x−5

y=(2*x−5)/8

y=1/4*x−5/8

3. Analyze the resulting function. The expression 1/4*x−5/8 is a polynomial (specifically, a linear function).

4. Determine the constraints. Polynomials are defined for all real numbers because there are no denominators containing x that could be zero and no even roots of negative numbers.

5. Conclude that the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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