They are mutually perpendicular. However, they need not intersect: if they are in different planes, they will not intersect.
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A horizontal line is a line perpendicular to the vertical.
Vertical is up and down and horizontal is side to side. Think of the horizon, it is a line and horizontal has the same root. In fact, one definition of horizontal is parallel to or in the plane of the horizon.
zero is horizontal, undefined is vertical
depends on whether y=6 or x=6 if y=6 then its a horizontal line if x=6 then its a vertical line
Diagonal means a line that is not vertical or horizontal, but in between. i.e. / or \