Find the Domain 6x=10y-30

Problem

6*x=10*y−30

Solution

1. Identify the type of equation. The given equation 6*x=10*y−30 is a linear equation in two variables.

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

10*y=6*x+30

y=(6*x+30)/10

y=3/5*x+3

3. Analyze the resulting function. The expression 3/5*x+3 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. State the domain in interval notation. Since there are no restrictions on the input x the domain is all real numbers.

Final Answer

Domain:(−∞,∞)

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