Find the Domain x+3y=8

Problem

x+3*y=8

Solution

1. Identify the type of equation. The equation x+3*y=8 represents a linear function.

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

3*y=−x+8

3. Divide by 3 to isolate y

y=−1/3*x+8/3

4. Determine the domain. Since the expression −1/3*x+8/3 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.

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

Final Answer

Domain:(−∞,∞)

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