please help with this word problem. i'm not understanding this concept and i have to show all of the work.

suppose x and y vary inversely, and y = 10 when x = 4. write a function that models the variation (1pt.). then find y when x = 90 (1pt.).
 
thank you

inverse relation:
 
xy = k,
 
where k is a constant.
 
x = 4 and y = 10 ⇒ k = xy = 4(10) = 40
 
xy = 40
 
y = 40/x
 
x = 90 ⇒ y = 40/90 = 4/9