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 |
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.