Find the slopes of the asymptotes of the hyperbola with the following equation.

36 = 9x ^{2} - 4y^{2}

You are given the equation 36 = 9x² + 4y². You are asked to find the slopes of the asymptotes of the hyperbola. A hyperbola has the following general equation x²/a² + y²/b² = 1. the goal here is to find the slopes of the hyperbolic equation. So divide both sides by 36

36 = 9x² + 4y²

(1/36) [36 = 9x² + 4y²]

1 = x²/4 + y²/9

a² = 4

a = 2

and

b² = 9

b = 3

To find the slope, divide a/b and you will get 2/3.