Answer
$x=2$
Work Step by Step
Recall:
A direct variation is represented by the equation $y=kx$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ also increases.
The equation that models the direct variation can be determined by solving the value of $k$:
This can be done by taking any ordered pair $(x, y)$ then substituting the values of $x$ and $y$ into the direct variation formula $y=kx$.
Since the variation contains the point $(4, 6)$, substitute these into the formula $y=kx$ to obtain:
\begin{align*}
y&=kx\\\\
6&=k(4)\\\\
\frac{6}{4}&=k\\\\
1.5&=k\end{align*}
Therefore, the equation that models the direct variation is $y=2.5x$.
To find the value of $x$ when $y=3$, substitute $3$ to $y$ in the equation above to obtain:
\begin{align*}
y&=1.5x\\\\
3&=1.5x\\\\
\frac{3}{1.5}&=\frac{1.5x}{1.5}\\\\
2&=x
\end{align*}
