## Ratios and the Constant of Proportionality

\[x, \: y\]

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 \[\frac{B}{A}\]

.