By definition, lines are parallel if they have the same gradient (slope). Any horizontal line has a gradient of 0, so it is parallel to any other horizontal line.
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The parallel line would also have a slope of zero (both are horizontal lines).
Horizontal lines have a slope of zero, and the slope of vertical lines is undefined. Parallel lines have equal slopes, and perpendicular lines have slopes that are negative reciprocals of each other. So we can say that: Two nonvertical lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the slopes are m1 and m2, then: m1 = - 1/m2 or (m1)(m2) = -1
Meaningless question. It sounds like a riddle rather than a maths problem. For an answer, assuming it is a riddle, I'd look at the letters that spell NINE. The six parallel lines are the vertical strokes of the letters; the extra five lines are the horizontal and diagonal strokes.
Horizontal lines always have a slope of 0.
A cone does not have any parallel lines