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.