Inverse variation is also known as inverse proportion. From the word "inverse", when the value of the variable increases, the other variable decreases. This relationship is described by the equation

`y= k/x`

where k is the proportionality constant, x and y are the variables.

Take note that k is any real number except zero. Also, the values of x and y can not also be zero.

Consider the following example:

It is given that a varies inversely with b. When a = 2, the value of b is 3.

(a) What is the equation of inverse variation that relates b to a?

(b) Do the values of b increases when the values of a changes from 1 to 0.5?

Solution:

(a) Apply the equation `y=k/x` . To do so, replace the variable x and y with a and b, respectively.

`b = k/a`

Plug in the given values of a and b.

`3 = k/2`

Then, solve for the proportionality constant, k.

`3*2 = k`

`6=k`

And, plug-in the value of k.

`b=6/a`

**Therefore, the equation of this inverse variation is `b = 6/a.` **

(b) To determine the values of b for each given value of a, plug in the values of a to the equation above.

`a = 1, b=6/1=6`

`a = 0.5, b=6/0.5 = 12`

So, the corresponding values of b are as follows:

a b

1 6

0.5 12

**Therefore, this verifies that as the values of a decreases, b increases.**

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