Suppose that x and y vary inversely and that x=10 when y=8. write the function that models the inverse variation. find y when x=5

As the variables vary inversely, we have the following relationship:
 
 From here, we must find the value of the constant k.
 For this, we use the following data:
 x = 10 when y = 8
 Substituting values we have:
 
 From here, we clear the value of k:
 
 Substituting the value of k we have that the function is:
 
 Then, for x = 5 we have:
 
 
 The function that models the inverse variation is:
 
 when x = 5: