Slope of line-parallel and perpendicular


Assignment:

As I have learned about parallel and perpendicular slopes, the slope is m=rise/run. Completely understand the perpendicular with a 90 degree offset. Can someone explain, why the rise/run is the same anywhere on the straight line? Is there a mathematical argument for this? If so/not then can someone explain? Any explanation is greatly appreciated.

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Algebra: Slope of line-parallel and perpendicular
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