1. **State the problem:** Find the slope of the line passing through the points $(-3, 2)$ and $(4, -5)$.\n\n2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:\n$$m = \frac{y_2 - y_1}{x_2 - x_1}$$\nThis formula calculates the "rise" over the "run" or the change in $y$ divided by the change in $x$.\n\n3. **Substitute the points:** Using $x_1 = -3$, $y_1 = 2$, $x_2 = 4$, and $y_2 = -5$, we get:\n$$m = \frac{-5 - 2}{4 - (-3)} = \frac{-7}{4 + 3}$$\n\n4. **Simplify the denominator:**\n$$m = \frac{-7}{7}$$\n\n5. **Simplify the fraction:**\n$$m = \cancel{\frac{-7}{7}} = -1$$\n\n6. **Interpretation:** The slope is $-1$, which means the line falls one unit vertically for every one unit it moves horizontally to the right. This matches the negative slope observed on the graph.