Find the Domain 2x-3y=5

Problem

2*x−3*y=5

Solution

1. Identify the type of equation. The equation 2*x−3*y=5 is a linear equation in two variables, which represents a straight line in the Cartesian plane.

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

3*y=2*x−5

y=2/3*x−5/3

3. Analyze the resulting function. The expression 2/3*x−5/3 is a polynomial of degree 1. Polynomial functions are defined for all real numbers because there are no denominators containing x that could be zero and no square roots of negative numbers.

4. Determine the domain. Since any real number x can be substituted into the equation to produce a valid real number y the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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