Any line with an undefined slope is parallel to the

Any line with an undefined slope is parallel to the y-axis.

Slope is a ratio between how much the line moves vertically to how much the line moves horizontally.

A line with an undefined slope has vertical movement but lacks horizontal movement. This makes the ratio look like this: 1/0. We know that it is impossible to divide any number by 0. Therefore the slope is undefined. 

A line with an undefined slope is just a vertical line on the x-y plane. The y-axis is also a vertical line on the x-y plane. Therefore, a line with an undefined slope is parallel to the y-axis.