What is a slope on a hill or mountain? Easy explanation.

📚 What is Slope?

Slope, in the context of a hill or mountain, refers to how steep it is. It's a measure of how much the elevation changes (vertical change) compared to the horizontal distance (horizontal change). A steeper hill has a larger slope, while a gentler hill has a smaller slope.

⛰️ Rise Over Run

The slope is calculated as 'rise over run'. 'Rise' is the vertical distance, and 'run' is the horizontal distance.

• 📐 Rise:
The vertical change in elevation. Think of it as how much higher you go.
• 🛤️ Run:
The horizontal distance covered. Think of it as how far you walk on level ground.
• ➗ Slope Formula: Slope = $\frac{Rise}{Run}$

📈 Interpreting Slope Values

The value of the slope tells us how steep the hill or mountain is:

• 🌳 Small Slope (close to 0):
This means a gentle incline, easy to walk up.
• 🧗 Large Slope (greater than 1):
This means a steep incline, hard to climb.
• 🚧 Slope of 1:
For every 1 unit of horizontal distance, you go up 1 unit vertically.

🧭 Examples in Real Life

• 🏞️ Gentle Hill:
A small rise over a large run (e.g., a hill that rises 10 meters over 100 meters of horizontal distance) has a small slope (10/100 = 0.1).
• 🌋 Steep Mountain:
A large rise over a small run (e.g., a mountain that rises 500 meters over 500 meters of horizontal distance) has a larger slope (500/500 = 1), and a mountain that rises 500 meters over 250 meters of horizontal distance has a larger slope of 2. This is much harder to climb!

💡 Calculating Slope: A Practical Example

Imagine you're hiking. After walking 100 meters horizontally, you check your altimeter and find you've climbed 20 meters vertically. What's the slope?

Slope = $\frac{Rise}{Run} = \frac{20 \text{ meters}}{100 \text{ meters}} = 0.2$

So, the slope is 0.2, which means it's a relatively gentle climb.

✅ Practice Quiz

Calculate the slope in the following scenarios:

1. You hike a hill, covering 50 meters horizontally and rising 5 meters vertically.
2. You climb a small mountain, covering 200 meters horizontally and rising 100 meters vertically.
3. A very steep hill rises 75 meters vertically over a horizontal distance of 25 meters.

Answers: 1) 0.1, 2) 0.5, 3) 3