Answer
$\dfrac{1}{2}$
Work Step by Step
Recall:
An inverse variation is represented by the equation $xy=k$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ decreases.
The equation that models the inverse variation can be determined by finding 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 inverse variation formula $xy=k$.
Since the variation contains the point $\left(4, 1.5\right)$, substitute these into the formula $xy=k$ to obtain:
\begin{align*}
xy&=k\\\\
4(1.5)&=k\\\\
6&=k\\\\
\end{align*}
Thus, the equation of the inverse variation is $xy=6$.
To find the value of $x$ when $y=12$, substitute $12$ to $y$ in the equation above to obtain:
\begin{align*}
xy&=6\\\\
x(12)&=6\\\\
\frac{x(12)}{12}&=\frac{6}{12}\\\\
y&=\frac{1}{2}\end{align*}
