Find the Domain 5x+8y=19

Problem

5*x+8*y=19

Solution

1. Identify the type of equation. This is a linear equation in two variables, which represents a straight line in the Cartesian plane.

2. Solve for y in terms of x to determine if there are any restrictions on the input values.

8*y=−5*x+19

y=−5/8*x+19/8

3. Analyze the resulting function. Since the expression −5/8*x+19/8 is a polynomial (specifically a linear function), it is defined for all real numbers. There are no denominators containing x that could be zero and no square roots of negative numbers.

4. Determine the domain. The domain of any linear function that is not a vertical line is the set of all real numbers.

Final Answer

Domain:(−∞,∞)

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