1. **State the problem:** Find the slope of the line passing through the points $(1, -7)$ and $(1, 13)$. 2. **Formula for slope:** 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:** $$m = \frac{13 - (-7)}{1 - 1} = \frac{13 + 7}{0} = \frac{20}{0}$$ 4. **Interpretation:** Division by zero is undefined, so the slope is undefined. 5. **Conclusion:** The line passing through these points is vertical, and vertical lines have an undefined slope. **Final answer:** The slope is **undefined**.