Find the Domain -x+3y=15

Problem

−x+3*y=15

Solution

1. Identify the type of equation. The equation −x+3*y=15 is a linear equation in two variables, which represents a straight line in the Cartesian plane.

2. Solve for y to express the equation in slope-intercept form.

−x+3*y=15

3*y=x+15

y=1/3*x+5

3. Determine the domain. The domain of a function is the set of all possible input values (x for which the function is defined.

4. Analyze the expression 1/3*x+5 Since this is a polynomial (specifically a linear function), there are no square roots of negative numbers, no denominators that could be zero, and no logarithms of non-positive numbers.

5. Conclude that x can be any real number.

Final Answer

Domain: *(−∞,∞)

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