1. **State the problem:** Find the equation of the line passing through the points $(-5,7)$ and $(-4,0)$ using the point-slope form. 2. **Recall the point-slope formula:** The equation of a line with slope $m$ passing through point $(x_1,y_1)$ is $$y - y_1 = m(x - x_1)$$ 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 7}{-4 - (-5)} = \frac{-7}{-4 + 5} = \frac{-7}{1} = -7$$ 4. **Use one point and the slope in the formula:** Using point $(-5,7)$, $$y - 7 = -7(x - (-5))$$ 5. **Simplify the equation:** $$y - 7 = -7(x + 5)$$ This is the point-slope form of the line through the given points. **Final answer:** $$y - 7 = -7(x + 5)$$