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

a. 7
b. -7
c. undefined
d. 0

The first point is (1,4) which means (x1,y1) = (1,4). So,
x1 = 1
y1 = 4

The second point is (1,-3) meaning that (x2,y2) = (1,-3). So,
x2 = 1
y2 = -3

Now use the slope formula. Plug in those four values mentioned above

m = (y2 - y1)/(x2 - x1)
m = (-3 - 4)/(1 - 1)
m = -7/0

This is where we run into issues. The denominator is 0. We CANNOT divide by zero. So the result is undefined.

Your calculator may say "UND" for "Undefined", it might say "NaN" for "Not a Number", or it might produce some other type of error. 

Choice C) undefined

Note: if you draw a line through the two given points, the line is completely vertical

The answer is option c.