1. **State the problem:** Find the equation of the line passing through the points $(2,-3)$ and $(2,6)$. 2. **Calculate the slope:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-3)}{2 - 2} = \frac{9}{0}.$$ Since division by zero is undefined, the slope is undefined. 3. **Interpret the slope:** An undefined slope means the line is vertical. 4. **Write the equation:** For a vertical line passing through $x=2$, the equation is $$x=2.$$