To find the slope of the line that passes through the two points \((-7, -2)\) and \((-15, -14)\), we can use the formula for the slope \(m\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign:
- \((x_1, y_1) = (-7, -2)\)
- \((x_2, y_2) = (-15, -14)\)
Now we substitute the values into the slope formula:
\[ m = \frac{-14 - (-2)}{-15 - (-7)} \]
This simplifies to:
\[ m = \frac{-14 + 2}{-15 + 7} \] \[ m = \frac{-12}{-8} \]
Now we can simplify \(\frac{-12}{-8}\):
\[ m = \frac{12}{8} = \frac{3}{2} \]
Therefore, the slope of the line that passes through the points \((-7, -2)\) and \((-15, -14)\) is
\[ \boxed{\frac{3}{2}}. \]