Answer
$k=.16$, $y=.16x$
Work Step by Step
If y varies directly as x, we know that the variables x and y can be related by the function $y=kx$, where k is the constant of proportionality.
If $y=.4$ when $x=2.5$, then we know that $.4=2.5k$ (or $\frac{2}{5}=\frac{5}{2}k$). Multiply both sides by $\frac{2}{5}$.
$k=\frac{2}{5}\times\frac{2}{5}=\frac{2\times2}{5\times5}=\frac{4}{25}=.16$
Therefore, the constant of variation is $k=.16$ and the direct variation equation is $y=.16x$.
