1. **Problem:** Find the gradient of the straight line joining points A (-4, -1) and B (4, 2). 2. **Formula:** The gradient $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Apply the formula:** $$m = \frac{2 - (-1)}{4 - (-4)} = \frac{2 + 1}{4 + 4} = \frac{3}{8}$$ 4. **Interpretation:** The gradient of the line joining A and B is $\frac{3}{8}$, meaning the line rises 3 units vertically for every 8 units it moves horizontally. Final answer: $\boxed{\frac{3}{8}}$