Question

18. A hot air balloon climbs into the air at a steady rate per minute. The graph illustrates the hot air balloon's ascent. Which example models the correct slope?
A) m = 20 − 12/10 − 6
B) m = 2 − 4/8 − 4
C) m = 10 − 6/20 − 12
D) m = 12 − 0/0 − 24

Answer 1

To find the correct slope of the hot air balloon's ascent from the options given, we need to apply the formula for slope, which is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the graph.

Let’s analyze each option:

A) \( m = \frac{20 - 12}{10 - 6} = \frac{8}{4} = 2 \)

B) \( m = \frac{2 - 4}{8 - 4} = \frac{-2}{4} = -\frac{1}{2} \)

C) \( m = \frac{10 - 6}{20 - 12} = \frac{4}{8} = \frac{1}{2} \)

D) \( m = \frac{12 - 0}{0 - 24} = \frac{12}{-24} = -\frac{1}{2} \)

To determine which option models a correct slope, consider if the slope is positive or negative and what the expected rate of ascent might be.

For a hot air balloon that climbs steadily, we would expect a positive slope.

From the calculations above:

- Option A gives a positive slope of 2, which indicates a steady ascent.
- Option C also gives a positive slope of \( \frac{1}{2} \).

Assuming that the graph shows a steady and positive climb, the slope from option A (m = 2) likely represents a steeper ascent.

Therefore, A would be the best answer if a steady ascent is expected. However, if less steep is acceptable, C is also a valid positive slope.

Thus, we conclude:

**A) m = 20 − 12/10 − 6** is the best option if we assume a consistent and noticeable ascent from the hot air balloon's graph.