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
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?
(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`
And, plug-in the value of k.
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:
Therefore, this verifies that as the values of a decreases, b increases.