Find the Domain 2x-3y+12=0

Problem

2*x−3*y+12=0

Solution

1. Identify the type of equation. The equation 2*x−3*y+12=0 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. Subtract 2*x and 12 from both sides.

−3*y=−2*x−12

3. Divide by −3 to isolate y

y=2/3*x+4

4. Determine the domain. In a linear function of the form y=m*x+b there are no square roots of negative numbers, no denominators that can be zero, and no logarithms. Therefore, the input x can be any real number.

5. Express the domain in interval notation. Since x can be any value from negative infinity to positive infinity, the domain is (−∞,∞)

Final Answer

Domain:(−∞,∞)

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