To find the slope of a line passing through two points, $(-2, 4)$ and $(4, -5)$, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

where $(x_1, y_1) = (-2, 4)$ and $(x_2, y_2) = (4, -5)$.

Substituting the values:

$m = \frac{-5 - 4}{4 - (-2)}$

$m = \frac{-9}{6}$

$m = -\frac{3}{2}$

So, the slope of the line passing through the points $(-2, 4)$ and $(4, -5)$ is:

$\boxed{-\frac{3}{2}}$

Would you like to see more details or have any questions? Here are some related problems:

1. Find the slope of a line passing through the points $(3, 7)$ and $(6, 2)$.
2. Determine the slope of a horizontal line passing through any two points.
3. What is the slope of a vertical line?
4. Find the equation of a line passing through $(-2, 4)$ and $(4, -5)$.
5. Calculate the slope of the line passing through the points $(0, 0)$ and $(5, 10)$.

Tip: The slope of a line measures how steep the line is. A negative slope indicates the line goes down from left to right.