\[x, \: y\]
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 \[\frac{B}{A}\]
.