Essay

Mathematical Consistency in Slope Determination

In a technical training manual for infrastructure surveying, it is emphasized that the slope of a grade is constant regardless of which direction the calculation is performed. Using the specific example of a line passing through the points (2, 3) and (7, 6), describe what happens to the values and signs of the 'rise' and the 'run' when you reverse the starting point (i.e., beginning the calculation at the rightmost point (7, 6) and moving to (2, 3)). Based on the procedure, explain the mathematical reason why the final slope remains 3/5.

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Updated 2026-04-19

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