Question

What kind of variation is $xy=c$ ?

Answer 1

Hint: Here we have to find the variation in the equation given. We have been given two unknown variables and a constant. Firstly fix the value of the constant and then for different values of $x$ check the value of $y$ . Finally see the relation between the two variables and get the desired answer.

Complete step by step solution:
The equation is given as follows:
$xy=c$…$\left( 1 \right)$
Now let us fix the value of the constant as follows:
$c=5$
Next we will take a different value of $x$ and check the pattern in values of $y$ .
Let $x=2$
Substitute $c=5,x=2$ in equation (1) as follows:
$\Rightarrow 4\times y=10$
$\Rightarrow y=\dfrac{5}{2}$
On simplifying we get,
$\Rightarrow y=2.5$
Next let $x=4$ substitute it in equation (1) we get,
$\Rightarrow 4\times y=5$
$\Rightarrow y=\dfrac{5}{4}$
So we get,
$\Rightarrow y=1.25$
So we can observe that when we are increasing the value of $x$ the value of $y$ is decreasing as for $x=2$ we are getting $y=2.5$ and for $x=4$ we are getting $y=1.25$ .
Hence the variation of the equation $xy=c$ is inverse variation.

Note:
Variation is a relation between a set of values of variables. It is the change in value of one variable on the other variable in an equation. Variation can be direct as well as inverse. In direct variation, one quantity varies directly as per the change in another quantity. In Inverse variation the first quantity varies inversely as per another quantity that is if one value is increasing another is definitely decreasing. It is generally written as $x\,\propto \dfrac{1}{y}$ .The only way to find the variation in an equation is to let the constant be any value and then for two or three values of one variable check the change in value of another variable.