1. **State the problem:** Find the gradient (slope) of the line passing through points $(-2, -5)$ and $(1, 4)$.\n\n2. **Formula for gradient:** The gradient $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:\n$$m = \frac{y_2 - y_1}{x_2 - x_1}$$\n\n3. **Substitute the points:** Here, $x_1 = -2$, $y_1 = -5$, $x_2 = 1$, and $y_2 = 4$. So,\n$$m = \frac{4 - (-5)}{1 - (-2)} = \frac{4 + 5}{1 + 2}$$\n\n4. **Simplify numerator and denominator:**\n$$m = \frac{9}{3}$$\n\n5. **Cancel common factors:**\n$$m = \frac{\cancel{9}^3}{\cancel{3}^1} = 3$$\n\n6. **Interpretation:** The gradient of the line is $3$, meaning the line rises 3 units vertically for every 1 unit it moves horizontally to the right.