Two points are all a line needs — and all its slope needs, too. Read aloud: m equals y-two minus y-one, over x-two minus x-one — $m = \dfrac{y_2 - y_1}{x_2 - x_1}$. The little numbers are labels, and they mean one thing all lesson: subscript 1 is the FIRST point, $(x_1, y_1)$, and subscript 2 is the second, $(x_2, y_2)$. Say them as names — $y_1$ is “y-one”, the first point's y. The top is the rise between the points, the bottom is the run — the same old friend, now wearing coordinates.

One rule keeps you safe here: pick an order and keep it. If point 2 leads on top, point 2 leads on the bottom too — mix the order and the sign of your slope lies to you. And the flip trap never retires: run over rise is NOT slope. When in doubt, whisper “rise over run” — the y's live upstairs.