## Ratios and the Constant of Proportionality

Suppose two quantities
$x, \: y$
related by a ratio, say
$A:B$
.
An quantites related in this way are proportional to each other. Where does the constant of proportionality appear?
The meaning of the ratio is this: If
$x$
is a multiple of
$A$
then
$y$
is that multiple of
$B$
so that
$\frac{x}{A}= \frac{y}{B}$
then
$y=\frac{B}{A} x$
and the constant of proportionality relating
$y$
to
$x$
is
$\frac{B}{A}$
.