# Is xy=4 a direct of inverse variation?

Apr 1, 2017

$x y = 4$ is an inverse variation

#### Explanation:

To understand the operation of this equation: $x y = 4$

the equation can be solved for a few values of $x$ or $y$.

Suppose we choose values for $x$ of $1 , \mathmr{and} 2 , \mathmr{and} 4$.

Then for $x = 1 , x y = 4 \to 1 y = 4 \to y = 4$
Then for $x = 2 , x y = 4 \to 2 y = 4 \to y = 2$
Then for $x = 4 , x y = 4 \to 4 y = 4 \to y = 1$

Suppose now we choose values for $y$ of $1 , \mathmr{and} 2 , \mathmr{and} 4$.

Then for $y = 1 , x y = 4 \to 1 x = 4 \to x = 4$
Then for $y = 2 , x y = 4 \to 2 x = 4 \to x = 2$
Then for $y = 4 , x y = 4 \to 4 x = 4 \to x = 1$

In either case we saw that as the value of $x$ increased, the value of $y$ decreased and vice versa, so the variation between the two is inverse.