# Constant of Variation

The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities.

The formula for direct variation is

$y=kx$ (or $y=kx$ )

where $k$ is the constant of variation .

Example 1:

If $y$ varies directly as $x$ and $y=15$ when $x=24$ , find $x$ when $y=25$ .

Find the constant of variation.

$\begin{array}{l}k=\frac{y}{x}=\frac{15}{24}=\frac{5}{8}\\ y=\frac{5}{8}x\end{array}$

To find $x$ , substitute $25$ for $y$ .

$\begin{array}{l}25=\frac{5}{8}x\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}x=40\end{array}$

The constant of variation in an indirect variation is the constant (unchanged) product between two variable quantities.

The formula for indirect variation is

$xy=k$ (or $y=\frac{k}{x}$ )

where $k$ is the constant of variation .

Example 2:

If it takes $4$ hours at an average speed of $90$ km/h to do a certain journey, how long would it take at $120$ km/h?

Find the constant of variation.

$k$ = speed · time

$k=90\cdot 4=360$

Then,