What is the slope of the line that passes through (1,4) and (1,-3)

Slope is calculated as the change in y over the change in x, or rise over run.

The change in y is the difference between the two given y-coordinates: 4 - (-3) = 7

The change in x is the difference between the two given x-coordinates (note that the order of the difference must be the same as the order of the difference of the y values): 1 - 1 = 0

So, 7/0 is the slope, but you cannot divide by 0, so the slope is undefined.