1. The problem asks to find the slope of the line segment between the points $(-3, -6)$ and $(0, 7)$ in the Cartesian coordinate system. 2. Recall that the slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Substitute the given points into the formula: $$m = \frac{7 - (-6)}{0 - (-3)} = \frac{7 + 6}{0 + 3} = \frac{13}{3}$$ 4. Simplify the fraction: $$m = \frac{13}{3} \approx 4.333$$ 5. Interpretation: The positive slope means the line rises steeply from left to right, consistent with the observation from the graph. Final answer: The slope of the line segment is $\boxed{\frac{13}{3}}$.