1. **State the problem:** Find the slope of the line passing through the points $(0, -8)$ and $(0, -10)$. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Substitute the given points:** $$m = \frac{-10 - (-8)}{0 - 0} = \frac{-10 + 8}{0} = \frac{-2}{0}$$ 4. **Interpret the result:** Division by zero is undefined in mathematics, so the slope is undefined. 5. **Conclusion:** Since the line is vertical (both points have the same $x$-coordinate), the slope is undefined. **Final answer:** The slope is undefined.