1. The problem asks for the slope of the line passing through points $D(-1, 9)$ and $G(4, 9)$. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Substitute the given points into the formula: $$m = \frac{9 - 9}{4 - (-1)} = \frac{0}{5}$$ 4. Simplify the fraction: $$m = 0$$ 5. Since the slope is zero, the line is horizontal. 6. Therefore, the slope of the line passing through points $D$ and $G$ is $0$.