Suppose that x and y vary inversely. Write a function rule for the function that models x=4 and y=8

Question

any information would be helpful I just really don't understand this 

Answer 1

Usually when two functions vary inversely they are of the form

 

y = k / x

 

wheere k is the constant of proportionality 

 

so in this case its

 

8 = k / 4

 

k = 32

 

now we can write this as a function

 

y = 32 / x

 

That's the function used to model inverse proportionality.

Answer 2

A familiar inverse relation is d = r · t. As you go faster it takes less time.

 

xy = k

4(8) = k

32 = k

 

xy = 32

Answer 3

To "vary directly," the value of y increases as a multiple of x and it decreases at the same rate.  That kind of function can be represented as y=kx for some constant k.  So, for example, when x=5 and y=10 then we know that k=2 and that y=50 when x=25 (that is, y=2x).

 

Now. to "vary inversely" means that y decreases as a multiple of x and it increases at the same rate.  This kind of a function can be represented as y=k(1/x) for some constant k.  In this example, when x=3 and y=8 then we know that k=24 and that when x goes up to x=4 the value of y=6 (that is, y=24/x).

 

This problem says that x and y vary inversely.  That means there is some value of k that makes this true:

             y = k(1/x)

 

We are given x=4 and y=8, so we know that:

             8 = k(1/4)

            4*8 = k                 [multiply both sides by 4]

              32 = k

That makes the function:

      y=32/x