Question

What is the slope of the line that passes through the points (3, 1) and (2, 5)?

Answer 1

\[\frac{y_2-y_1}{x_2-x_1}\]

Say
\[(x_1,y_1) \:\;\;is \:\;\; (3,1)\] and
\[(x_2,y_2) \:\;\;is \:\;\; (2,5)\]
Note: it does not matter which one is the first or second, they will both end up being the same slope, just be consistent throughout the problem.
So:

\[\frac{y_2-y_1}{x_2-x_1}=\frac{5-1}{2-3}=\frac{4}{-1}=-4\]