Ask a New Question
Menu

Question 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? (1 point) Responses m=12−00−24m=12−00−24m is equal to the fraction with numerator 12 minus 0 and denominator 0 minus 24 m=20−1210−6m=20−1210−6m is equal to the fraction with numerator 20 minus 12 and denominator 10 minus 6 m=2−48−4m=2−48−4m is equal to the fraction with numerator 2 minus 4 and denominator 8 minus 4 m=10−620−12m=10−620−12m is equal to the fraction with numerator 10 minus 6 and denominator 20 minus 12 Skip to navigation Item 1 , Fully Attempted. Item 2 , Fully Attempted. Item 3 , Fully Attempted. Item 4 , Fully Attempted. Item 5 , Fully Attempted. Item 6 , Fully Attempted. Item 7 , Fully Attempted. Item 8 , Fully Attempted. Item 9 , Fully Attempted. Item 10 , Fully Attempted. Item 11 , Fully Attempted. Item 12 , Fully Attempted. Item 13 , Fully Attempted. Item 14 , Fully Attempted. Item 15 , Fully Attempted. Item 16 , Fully Attempted. Item 17 , Fully Attempted. Item 18 , Unattempted. Previous Review

1 answer

To find the correct slope for the ascent of the hot air balloon, we need to use the slope formula:

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

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

Let's analyze the options you provided:

  1. \( m = \frac{12 - 0}{0 - 24} \)
  2. \( m = \frac{20 - 12}{10 - 6} \)
  3. \( m = \frac{2 - 4}{8 - 4} \)
  4. \( m = \frac{10 - 6}{20 - 12} \)

We'll simplify each option:

  1. \( m = \frac{12 - 0}{0 - 24} = \frac{12}{-24} = -\frac{1}{2} \)
  2. \( m = \frac{20 - 12}{10 - 6} = \frac{8}{4} = 2 \)
  3. \( m = \frac{2 - 4}{8 - 4} = \frac{-2}{4} = -\frac{1}{2} \)
  4. \( m = \frac{10 - 6}{20 - 12} = \frac{4}{8} = \frac{1}{2} \)

Now, assuming the hot air balloon is ascending, we are looking for a positive slope. The only option with a positive slope is:

Option 2: \( m = \frac{20 - 12}{10 - 6} = 2 \)

Thus, the correct model for the slope of the hot air balloon's ascent is:

Answer: \( m = \frac{20 - 12}{10 - 6} \) or \( m = 2 \)