Slope From Two Points

You can find the rise and the run by subtracting coordinates. This gives the slope formula. For a line through two points, the slope is the difference of the y values divided by the difference of the x values. Subtract in the same order on the top and on the bottom:

$$m = \frac{y\cdot 2-y\cdot 1}{x\cdot 2-x\cdot 1}$$

For the line through (2, 7) and (5, 1), take (5, 1) as the second point: $m = \frac{1-7}{5-2} = \frac{-6}{3} = -2$. You can also take (2, 7) as the second point, and the answer is the same: $\frac{7-1}{2-5} = \frac{6}{-3} = -2$. Either order works, as long as you use the same order on the top and on the bottom.

Do not mix the two orders. If you write $y\cdot 2-y\cdot 1$ on top and $x\cdot 1-x\cdot 2$ on the bottom, the slope comes out with the wrong sign. Choose one order, and use it for both subtractions.