1. **State the problem:** Find the slope of the line passing through the points $(-1,4)$ and $(4,-3)$. 2. **Formula for slope:** The slope $m$ 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. **Identify points:** Here, $x_1 = -1$, $y_1 = 4$, $x_2 = 4$, and $y_2 = -3$. 4. **Calculate the difference in $y$ values:** $$y_2 - y_1 = -3 - 4 = -7$$ 5. **Calculate the difference in $x$ values:** $$x_2 - x_1 = 4 - (-1) = 4 + 1 = 5$$ 6. **Calculate the slope:** $$m = \frac{-7}{5} = -\frac{7}{5}$$ 7. **Interpretation:** The slope is negative, indicating the line descends from left to right. **Final answer:** The slope of the line is $-\frac{7}{5}$.