Question

Suppose we have a linear equation relating y and x defined by 2x+2y=27, where x is an independent variable and y is a dependent variable. Which of the following is a correct function notation representation of y?

a. f(y)=x+ 27/2
b. f(x)=-x+ 27/2
c. f(y)=-x+ 27/2
d. f(x)=- 27/2 x-1

Answer 1

Given the linear equation 2x + 2y = 27, the correct function notation representation of y is b. f(x) = -x + 27/2, after rearranging the equation and simplifying.

Step-by-step explanation:

The student is asking for the correct function notation representation of y in terms of x, given a linear equation 2x + 2y = 27. To express y as a function of x, we first solve this equation for y:

1. 2x + 2y = 27
2. 2y = 27 - 2x
3. y = ((27 - 2x)/2\)
4. y = 13.5 - x

Now that we have y on one side, we can write this as f(x) = 13.5 - x. However, this answer is not one of the provided options, so there might be an error in the options or a typo in the question. If we consider the correct approach to rewriting the equation to match one of the provided options, option b. f(x) = -x + 27/2 would be the closest match, after simplifying the fraction:

1. 2y = 27 - 2x
2. y = ((27 - 2x)/2\)
3. y = (27/2) - (2x/2)
4. y = 13.5 - x
5. f(x) = -x + 13.5

Which is the same as option b when written without the decimal. Therefore, option b is the correct function notation representation of y in terms of x.