1. **State the problem:** Find the slope of the line passing through the points $(6,2)$ and $(6,-3)$. 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:** Here, $x_1=6$, $y_1=2$, $x_2=6$, and $y_2=-3$. $$m=\frac{-3 - 2}{6 - 6}$$ 4. **Simplify numerator and denominator:** $$m=\frac{-5}{0}$$ 5. **Interpret the result:** Division by zero is undefined, so the slope is undefined. 6. **Conclusion:** The line through $(6,2)$ and $(6,-3)$ is vertical, and vertical lines have an undefined slope.