# Path Slope

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#### What’s the point?

The word “slope” in math has exactly the same meaning as in normal life. It’s just how far up you go up compared to how far you go forward.

#### TL;DW

• The mathematical definition of slope is:

$\mathbf{slope}\ =\ \frac{\mathbf{vertical}\ \mathbf{change}}{\mathbf{horizontal}\ \mathbf{change}}$

• On a flat surface, there’s no up and down motion as you move horizontally, we’d say there is no slope or more exactly, the slope is zero.

$\mathbf{slope}\ =\ \frac{\mathbf{0}}{\mathbf{100}}\ =\ \mathbf{0}$

• Going up a hill, you move vertically up as you move forward. It’s a slope, or more exactly, the slope is positive. If you gain 10 meters in altitude for every 100 meters you walk forward:

$\mathbf{slope}\ =\ \frac{\mathbf{10}}{\mathbf{100}}\ =\ \mathbf{.10}$

• Descending a hill, you also move vertically as you move forward, but down this time. It’s also a slope, but more exactly we’d say it had a negative slope. If you descend 10 meters for every 100 meters you walk forward:

$\mathbf{slope}\ =\ \frac{\mathbf{-10}}{\mathbf{100}}\ =\ \mathbf{-.10}$

### Where To:

Khan has lots of examples!