1. The problem asks to find the slope of the graph of a vertical line at $x=3$. 2. Recall that the slope $m$ of a line is given by the formula: $$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. For a vertical line, the $x$-coordinate is constant, so $x_2 - x_1 = 0$. 4. Substituting into the slope formula, we get: $$m = \frac{y_2 - y_1}{\cancel{0}}$$ 5. Division by zero is undefined in mathematics, so the slope of a vertical line is undefined. 6. Therefore, the slope of the graph at $x=3$ is \textbf{undefined}.