Find the Domain 9x-8y=40

Problem

9*x−8*y=40

Solution

1. Identify the type of equation. The equation 9*x−8*y=40 is a linear equation in two variables.

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

8*y=9*x−40

y=9/8*x−5

3. Analyze the resulting function. The expression 9/8*x−5 is a polynomial (specifically, a linear function).

4. Determine the restrictions. 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 the domain. Since there are no restrictions on the input x the domain consists of all real numbers.

Final Answer

Domain: *(−∞,∞)

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