$\"\"$

Observe the graphs :

If the transverse axis is horizontal, the distance between the two vertices $\"\"$ is a horizontal distance and $\"\"$ is a vertical distance.

Therefore, the slopes of the asymptotes are equal to the rise over the run or $\"\"$ .

If the transverse axis is vertical, then $\"\"$ is a vertical distance and $\"\"$ is a horizontal distance.

Therefore, the slopes of the asymptotes are $\"\"$ .