The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\dfrac{y_2 - y_1}{x_2 - x_1}$. In this case, the points are $(9, 4)$ and $(2, 12)$, so the slope is \[\dfrac{12 - 4}{2 - 9} = \dfrac{8}{-7} = \boxed{-\dfrac{8}{7}}.\]
