# What is the constant of proportionality "k"?

Nov 11, 2014

Direct Variation

If $y$ is directly proportional to $x$, then we can write

$y = k x$,

where $k$ is the constant of proportionality.

If you solve for $k$, we have

$k = \frac{y}{x}$,

which is the ratio of $y$ to $x$.

Hence, the constant of proportionality is the ratio between two quantities that are directly proportional.

Inverse Variation

If $y$ is inversely proportional to $x$, then we can write

$y = \frac{k}{x}$,

where $k$ is the constant of proportionality.

If you solve for $k$, we have

$k = x y$,

which is the product of $x$ and $y$.

Hence, the constant of proportionality is the product of quantities that are inversely proportional.

I hope that this was helpful.