Question

The given pair of value form an inverse variation. Find the missing value:
$(2,5),(4,y)$

Answer 1

The statement " $y$ varies inversely as $x$ means that when $x$ increases, $y$ decreases by the same factor. In other words, the expression $xy$ is constant:

$xy=k$

where $k$ is the constant of variation.

Here, it is given that $x=2$ is inversely proportional to $y=5$, therefore,

$xy=k\Rightarrow 2\times 5=k\Rightarrow k=10$

Thus, the general equation is $xy=10$.

Since $x=4$, therefore,

$xy=10\Rightarrow 4y=10\Rightarrow y=\frac{10}{4}=2.5$

Hence, $y=2.5$ when $x=4$.