Explore: Algebra Lab, Rate of Change of a Linear Function
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What should we change to make the slope less steep?
Example Solution:
| Rise | Run |
|---|---|
| 12 | 24 |
| 8 | 24 |
| 18 | 30 |
We are given a skateboard ramp with a rise of 18 inches and a run of 24 inches. The ratio riserun gives us the slope of the ramp.
m=18/24 ⇔ m=3/4
We are asked to list three different sets of riserun measurements that will result in a less step ramp. Notice that there are two options for changing the dimensions of the ramp in order to make it less steep.
Decrease the vertical distance. This will make the ramp less steep if the horizontal distance is kept the same. Therefore, if we choose a vertical distance that is less than 18, we will get a less steep ramp. Let's take the vertical distance equal to 12 and 8.
| Rise | Run | Rise/Run | Evaluate |
|---|---|---|---|
| 12 | 24 | 12/24 | 0.5 |
| 8 | 24 | 8/24 | 0.333333... |
As we can see, both of them are less than the original ratio 34, which evaluates to 0.75.
Another way of making the ramp less steep is to increase the horizontal distance and keep the vertical distance the same. Therefore, we can choose a horizontal distance that is greater than 24. Let's take 30. Rise/Run = 18/30 = 0.6 As we can see, this horizontal distance also gives us a ratio that is less than than the original one.