*Contributor: Jonathan Heagy. Lesson ID: 12674*

As the owner of a new ski resort, you need to classify the steepness of the mountains to keep customers safe and happy. This lesson will teach you how to find the slope of a line using two points!

categories

subject

Math

learning style

Visual

personality style

Otter

Grade Level

Middle School (6-8)

Lesson Type

Dig Deeper

Have you ever been skiing? It's a great way to get outside and have fun in the winter or when visiting cold, mountainous areas. Whether you've been or not, you may know that ski slopes are classified by how steep they are. The three most common classifications of ski slopes are "green circle" for beginners, "blue square" for intermediate skiers, and "black diamond" for the more advanced skiers. Classifying these correctly is extremely important, because it helps keep skiers safe! So, imagine you just bought your own ski resort, and you need to classify the difficulty of your slopes in order to get up and running! On a separate piece of paper, brainstorm a name for your resort and write down a few ideas about how you think you might use math to plot out the design of the various slopes at your new resort.

So, what are your ideas?

Frosty Mountain Trail? Blizzard Blast? Bunny Hop Hijinks?

- How are the slopes and the difficulty levels going to reflect the name?
- What about the math? How does that come into the play of your resort design?

It turns out, the math concept actually shows up in a pretty obvious place! You classify ski *slopes* by finding the *slope*! But what does this mean?

**Slope** is a measure of steepness and can be either positive or negative. Another way to think of it is "rise over run," meaning to find the slope you take the change in vertical height divided by the change in horizontal distance between your two points. If you want to find the slope between two points (x_{1},y_{1}) and (x_{2},y_{2}), then the slope is equal to (y_{2}-y_{1}) ÷ (x_{2}-x_{1}). Another way to think of slope is by calling it the *rate of change*, or the speed at which something changes. If you hear someone say "slope" or "rate of change," they are referring to the same thing.

Let's try an example of finding a slope:

- Say you want to find the slope of the line connecting the points (1,3) and (11,33). Start by identifying your (x
_{1},y_{1}) and (x_{2},y_{2}) values. x_{1}=1, y_{1}=3, x_{2}=11, and y_{2}=33. It doesn't matter which x-values are x_{1}and x_{2}and which y-values are y_{1}and y_{2}, the answer will come out the same regardless! - Next, plug your values into the slope equation. (y
_{2}-y_{1}) ÷ (x_{2}-x_{1}) = (33-3) ÷ (11-1). - Finally, solve! (33-3) ÷ (11-1) = 30 ÷ 10 = 3, so the slope of your line is 3!

Can you think of a career (outside of ski resort owner) where you might use slopes in your everyday work?

Schuss on over to the *Got It?* section to continue working on your ski resort.

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