Answer
The equation matches with the graph labeled as II.
Work Step by Step
$16y^2-x^2=144$
$\frac{x^2}{9}-\frac{y^2}{144}=1$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$a^2=9$
$a=3$
Vertices: $(0,±a)=(0,±3)$
The hyperbole with vertices in $(0,±3)$ is the graph labeled as II.
