Find the Domain 5x-6y=15

Problem

5*x−6*y=15

Solution

1. Identify the type of equation. The given equation 5*x−6*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 function notation y=ƒ(x)

5*x−6*y=15

−6*y=−5*x+15

y=5/6*x−15/6

y=5/6*x−5/2

3. Analyze the resulting function ƒ(x)=5/6*x−5/2 This is a polynomial function of degree 1.

4. Determine the domain. Since there are no square roots of negative numbers, no logarithms of non-positive numbers, and no denominators that can equal zero (the denominator is a constant 6), the function is defined for all real numbers.

5. Express the domain in interval notation. The set of all real numbers is written as (−∞,∞)

Final Answer

Domain: *(−∞,∞)

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