Why does it naturally follow from
That lines having the same slope are parellel?
Apparently the same applies for cot and perpendicular lines.
I don't see it.
Let a and b be the angle each line makes with the horizontal
The slope of a line m = dy/dx = tan(a) or tan(b)
if the lines have the same slope tana = tanb
therefore tan(a-b) = 0
a-b = 0
a = b
i.e the lines are parallel as they make the the same angle with respect to the horizontal