Question

Suppose that x and y vary inversely, and x = 2 when y = 7. Write the function that models the inverse variation.

Answer 1

The answer to the question is letter B. y=14/x

Answer 2

Since, in this case, we have 4 options then you just need to substitute each number.
A. y = 5/x
B. y = 14/x
C. y = 9/x
D. y = 3.5x
 
We know that x= 2 when y=7. So...
A. y = 5/x
    7=5/2
    7=2.5 
   This is false.

B. y = 14/x
    7= 14/2
    7=7
  This is right, So True.

C. y = 9/x
     7=9/2
     7=4.5
    False

D. y = 3.5x    7=3.5(2)
    7=7
  This one is also true.

In this case we look for definition.

he statement " y varies inversely as x means that when x increases, y decreases by the same factor. In other words, the expression xy is constant:
xy = k   

where k is the constant of variation.

We can also express the relationship between x and y as:

y =  k/x 

where k is the constant of variation.