Find the Domain 5y+4x=6

Problem

5*y+4*x=6

Solution

1. Identify the type of equation. The equation 5*y+4*x=6 is a linear equation in two variables.

2. Solve for y to express the equation as a function of x Subtract 4*x from both sides and divide by 5

5*y=−4*x+6

y=−4/5*x+6/5

3. Analyze the resulting function. The expression −4/5*x+6/5 is a polynomial of degree 1.

4. Determine the restrictions. 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 linear function (that is not a vertical line) is all real numbers.

Final Answer

Domain: *(−∞,∞)

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