Ski Slope Slopes!

Lesson Plan - Get It!

Audio:

• So, what are your ideas?

I though of Frosty Mountain Trail, Blizzard Blast, and 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 (x₁,y₁) and (x₂,y₂), then the slope is equal to (y₂-y₁) ÷ (x₂-x₁).

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:

1. Say you want to find the slope of the line connecting the points (1,3) and (11,33).

Start by identifying your (x₁,y₁) and (x₂,y₂) values.

x₁=1

y₁=3

x₂=11

y₂=33

It doesn't matter which x-values are x₁ and x₂ and which y-values are y₁ and y₂, the answer will come out the same regardless!

2. Next, plug your values into the slope equation.

(y₂-y₁) ÷ (x₂-x₁) = (33-3) ÷ (11-1)

3. Finally, solve!

(33-3) ÷ (11-1) = 30 ÷ 10 = 3

So the slope of your line is 3!

Great work!

• 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.