Slope and intercepts
Slope is the change in y over the change in x; in y = mx + b, b is the y-intercept.
A worked example
Through (-3, 5) and (1, -7) the slope is (-7 - 5) / (1 - (-3)) = -12/4 = -3.
The mistake people actually make
Subtract the coordinates in the same order top and bottom, or the sign flips. The y-intercept is found by setting x = 0, the x-intercept by setting y = 0.