Find the Domain 3x+8y=24

Problem

3*x+8*y=24

Solution

1. Identify the type of equation. The equation 3*x+8*y=24 is a linear equation in two variables, which represents a straight line in the Cartesian plane.

2. Solve for y to express the equation as a function of x Subtract 3*x from both sides and divide by 8

8*y=−3*x+24

y=−3/8*x+3

3. Analyze the resulting function ƒ(x)=−3/8*x+3 This is a polynomial function of degree 1.

4. Determine the constraints on the input x Since there are no denominators containing x no square roots of negative numbers, and no logarithms, the function is defined for all real numbers.

5. State the domain in interval notation. The domain of any non-vertical linear function is the set of all real numbers.

Domain=(−∞,∞)

Final Answer

Domain of *3*x+8*y=24* is *(−∞,∞)

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