The slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$\frac{y_2-y_1}{x_2-x_1}.$$ In this case, the two points are $(-4,-7)$ and $(-2,-19)$. Plugging these values into the slope formula, we have $$\frac{-19-(-7)}{-2-(-4)} = \frac{-19+7}{-2+4}= \frac{-12}{2} = \boxed{-6}.$$
