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The Slope of the Line: Parallel and Perpendicular

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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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Solution Summary

Explaining the concept of the "slope of a line" and how/why it is constant for any two points along the line. Two jpeg files are also attached to assist with this solution.

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Before getting into the mathematics of why a slope is constant upon a straight line let us think about a real life example. Suppose you are on a flat surface walking. Consider this flat surface to be a line you are walking on. Suppose for reference there is a hill next to you. You walk on this line for 10 miles and notice you are still at the same elevation from the reference hill. You have ...

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