31. Across a horizontal distance of 20 feet, a roller coaster has a steep drop. The height of the roller coaster at the bottom of the drop is -100 feet, compared to its height at the top of the drop. What is the average amount that the roller coasters height drops over each horizontal foot?

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The change in height (vertical drop) is $$ -100 $$ feet, and the horizontal distance is $$ 20 $$ feet.

The average drop per horizontal foot is given by the slope, calculated as:
$$
\text{slope} = \frac{\text{change in height}}{\text{horizontal distance}} = \frac{-100}{20} = -5.
$$

Thus, the roller coaster’s height drops an average of $$ 5 $$ feet for every horizontal foot traveled (the negative sign indicates the drop).
The roller coaster drops an average of 5 feet for every horizontal foot traveled.

31. Across a horizontal distance of 20 feet, a roller coaster has a steep drop. The height of the roller coaster at the bottom of the drop is -100 feet, compared to its height at the top of the drop. What is the average amount that the roller coasters height drops over each horizontal foot?

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