Slope From Two Points

Rise and run are subtractions, so slope has a formula. Through two points, the slope is the difference of the y values over the difference of the x values, taken in the same order:

m = (y2 - y1)/(x2 - x1)

Through (2, 7) and (5, 1): m = (1 - 7)/(5 - 2) = -6/3 = -2. The order does not matter as long as it matches: (7 - 1)/(2 - 5) gives 6/(-3), the same -2.

The one mistake worth naming: mixing the orders, y2 - y1 over x1 - x2, flips the sign. Pick an order, use it on top and bottom, and the sign takes care of itself.