1. **Problem Statement:** Show that if a line passes through points $(x_1, y_1)$ and $(h, k)$ with slope $m$, then the equation $k - y_1 = m (h - x_1)$ holds. 2. **Formula for slope:** The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Apply the formula to given points:** Here, the two points are $(x_1, y_1)$ and $(h, k)$, so: $$m = \frac{k - y_1}{h - x_1}$$ 4. **Rearranging the equation:** Multiply both sides by $(h - x_1)$ to isolate the numerator: $$m (h - x_1) = k - y_1$$ 5. **Conclusion:** This shows that the difference in the $y$-coordinates equals the slope times the difference in the $x$-coordinates, which is exactly the statement to prove: $$k - y_1 = m (h - x_1)$$ This formula is fundamental in coordinate geometry and expresses the relationship between slope and coordinates of points on a line.