Find the Domain 7x-5=4y-6

Problem

7*x−5=4*y−6

Solution

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

2. Solve for y in terms of x to express the relation as a function y=ƒ(x)

3. Isolate the y term by adding 6 to both sides of the equation.

7*x−5+6=4*y

7*x+1=4*y

4. Divide both sides by 4 to solve for y

y=(7*x+1)/4

5. Analyze the resulting function. Since ƒ(x)=7/4*x+1/4 is a linear polynomial, there are no values of x that cause division by zero or result in non-real numbers.

6. Determine the domain. The function is defined for all real numbers.

Final Answer

Domain: *(−∞,∞)

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