Question

Suppose that x and y vary inversely and x = 1 when y = 12. Write a function that models the inverse variation. Graph the function and find y when x = 20.
Write a function that models the inverse variation.

Answer 1

An inverse variation in its generic form can be for example:
 y = k / x
 We observe that we must find the value of k.
 For this, we use the following fact:
 "x = 1 when y = 12"
 Substituting we have:
 12 = k / 1
 Therefore k = 12
 Thus, the equation is:
 y = 12 / x
 For x = 20 we have:
 y = 12/20
 y = 6/10
 y = 3/5
 y = 0.6
 Answer:
 when x = 20, and is:
 y = 0.6
 See attached graph.