If the slope of two lines doesn’t exist, what is their relative position with each other and with respect to x-axis and y-axis respectively?

The standard equation of a line is y=m*x+b, where m is the slope. If m does not exist then m = NULL and y=b1 and y=b2. This means the 2 lines are both horizontal, such that they are parallel with each other and also with the x-axis. This also means that the two lines are perpendicular to the y-axis.