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1. Parallel lines have equal slopes but different y-intercepts, while perpendicular lines have slopes that are negative reciprocals of each other. The relationship between slopes and y-intercepts helps distinguish between parallel and perpendicular lines.
2. When the slopes and y-intercepts are the same, the lines coincide and become a single line. This results in identical lines rather than two distinct lines.
3. The relationship of y-intercepts in perpendicular lines is not crucial as perpendicularity is determined by the slopes, not the y-intercepts. Different y-intercepts do not affect the perpendicular nature of the lines.
4. Three distinct lines cannot be perpendicular to each other simultaneously. If two lines are perpendicular, adding a third perpendicular line would result in all three lines intersecting at one point, which is not possible for distinct lines.
5. Parallel and perpendicular lines are commonly found in architecture, like in building designs where parallel lines represent walls or beams, and perpendicular lines indicate corners or intersecting walls. In urban planning, roads often form parallel and perpendicular patterns, aiding in traffic flow and city layout.