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=2−4/8−4
m is equal to the fraction with numerator 2 minus 4 and denominator 8 minus 4

m=20−12//10−6
m is equal to the fraction with numerator 20 minus 12 and denominator 10 minus 6

m=12−0/0−24
m is equal to the fraction with numerator 12 minus 0 and denominator 0 minus 24

m=10−6/20−12

Answer 1

To determine which example models the correct slope for the hot air balloon's ascent, we need to find the change in height divided by the change in time.

The formula for the slope (m) is given as:
\[ m = \frac{\text{change in height}}{\text{change in time}} \]

Let's evaluate the provided options:

1. \( m = \frac{2 - 4}{8 - 4} \)
- Change in height: \( 2 - 4 = -2 \)
- Change in time: \( 8 - 4 = 4 \)
- \( m = \frac{-2}{4} = -0.5 \)

2. \( m = \frac{20 - 12}{10 - 6} \)
- Change in height: \( 20 - 12 = 8 \)
- Change in time: \( 10 - 6 = 4 \)
- \( m = \frac{8}{4} = 2 \)

3. \( m = \frac{12 - 0}{0 - 24} \)
- Change in height: \( 12 - 0 = 12 \)
- Change in time: \( 0 - 24 = -24 \)
- \( m = \frac{12}{-24} = -0.5 \)

4. \( m = \frac{10 - 6}{20 - 12} \)
- Change in height: \( 10 - 6 = 4 \)
- Change in time: \( 20 - 12 = 8 \)
- \( m = \frac{4}{8} = 0.5 \)

Now that we have computed the slopes:

- First option: -0.5
- Second option: 2
- Third option: -0.5
- Fourth option: 0.5

Assuming the hot air balloon is supposed to have a positive ascent (climbing up), the only viable option would be the second one, where \( m \) equals 2.

Thus, the response that models the correct slope for the hot air balloon's ascent is:

**m = \( \frac{20 - 12}{10 - 6} \)**

This indicates that the balloon is climbing upwards at a rate of 2 (units of height per unit of time).