### Instruction: The hyperbola given by the equation \[\frac{y^2}{9}-\frac{x^2}{4} = 1\]has asymptotes $y = \pm mx,$ where $m$ is positive. Find $m.$.### Response: To find the asymptotes of a hyperbola, I need to use the coefficients of the $y^2$ and $x^2$ terms in the equation.
The general form of the asymptotes for a hyperbola of the form \[\frac{y^2}{a^2}-\frac{x^2}{b^2} = 1\] is $y = \pm \frac{a}{b}x.$
In this case, $a^2 = 9$ and $b^2 = 4,$ so the asymptotes are $y = \pm \frac{3}{2}x.$
Therefore, $m = \frac{3}{2}.$