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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 Preview

    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 ...

    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.