Find the Domain 0.4x-0.5y=3.7

Problem

0.4*x−0.5*y=3.7

Solution

1. Identify the type of equation. This is a linear equation in two variables, x and y

2. Determine the variable for which the domain is being sought. In the context of a function y=ƒ(x) the domain refers to all possible real values of the independent variable x

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

0.4*x−0.5*y=3.7

−0.5*y=−0.4*x+3.7

y=(−0.4*x)/(−0.5)+3.7/(−0.5)

y=0.8*x−7.4

4. Analyze the resulting function. Since y=0.8*x−7.4 is a polynomial (specifically a linear function), there are no square roots of negative numbers, no divisions by zero, and no logarithms of non-positive numbers.

5. Conclude that x can be any real number.

Final Answer

Domain: *(−∞,∞)

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