1. The problem is to find the equation of the line passing through the points $(-3, 4)$ and $(2, -1)$. 2. The formula to find the slope $m$ of a line passing through 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 slope formula: $$m = \frac{-1 - 4}{2 - (-3)} = \frac{-5}{5} = -1$$ 4. Now use the point-slope form of the line equation: $$y - y_1 = m(x - x_1)$$ 5. Using point $(-3, 4)$ and slope $m = -1$: $$y - 4 = -1(x - (-3))$$ $$y - 4 = -1(x + 3)$$ 6. Simplify the equation: $$y - 4 = -x - 3$$ $$y = -x - 3 + 4$$ $$y = -x + 1$$ 7. The equation of the line passing through the points $(-3, 4)$ and $(2, -1)$ is: $$y = -x + 1$$