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How and why is Rise/Run gives the inclination of the line (or slope)? How to understand the theoratical concept behind it ?

learner
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    $\frac{\text{rise}}{\text{run}}$ can be thought of as $\frac{\Delta y}{\Delta x}$ which is the the change in $y$ for each unit increase in $x$. – Landuros Apr 11 '20 at 05:50
  • Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Apr 11 '20 at 05:53
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    Let's say you're walking uphill. If you move 5 meters vertically for every 3 meters that you move horizontally, then the path you're walking on is very steep. On the other hand, if you move 1 meter vertically for every 3 meters that you move horizontally, the path you're walking on is much less steep. The "grade" (steepness) of roads is measured like this: https://en.wikipedia.org/wiki/Grade_(slope) – littleO Apr 11 '20 at 05:57

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It's a definition. We define the slope to be the rise over the run. This way a positive slope is a higher number when it's steeper, which is nice. But we could very well have defined it as "run" over "rise".

Mike Pierce
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