To find the slope of a line given two points, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, the two points are \((-5, -2)\) and \((4, -8)\). We can assign:
\[ (x_1, y_1) = (-5, -2) \] \[ (x_2, y_2) = (4, -8) \]
Now, let's substitute these coordinates into the formula:
- Calculate \( y_2 - y_1 \):
\[ y_2 - y_1 = -8 - (-2) = -8 + 2 = -6 \]
- Calculate \( x_2 - x_1 \):
\[ x_2 - x_1 = 4 - (-5) = 4 + 5 = 9 \]
- Substitute these results into the slope formula:
\[ m = \frac{-6}{9} \]
- Simplify the fraction:
\[ m = -\frac{2}{3} \]
Thus, the slope of the line connecting the points \((-5, -2)\) and \((4, -8)\) is
\[ \boxed{-\frac{2}{3}} \]