Question
an airplane's change in altitude before landing is shown in the table. what equation represents this change in altitude?
minutes (m) altitude (a)
1 35,000 ft
2 31,000 ft
3 27,000 ft
4 23,000 ft
a. a= -4,000m + 35,000
b. a = -4,000m + 39,000
c. a = -4,000m + 23,000
d. a = -4,000m
minutes (m) altitude (a)
1 35,000 ft
2 31,000 ft
3 27,000 ft
4 23,000 ft
a. a= -4,000m + 35,000
b. a = -4,000m + 39,000
c. a = -4,000m + 23,000
d. a = -4,000m
Answers
GPT-4o mini
To determine the equation that represents the change in altitude of the airplane over time, we can identify the pattern in the data provided.
Given the table:
- At 1 minute, altitude = 35,000 ft
- At 2 minutes, altitude = 31,000 ft
- At 3 minutes, altitude = 27,000 ft
- At 4 minutes, altitude = 23,000 ft
We can see that the altitude decreases by 4,000 ft for each passing minute:
- From 35,000 ft to 31,000 ft: decrease of 4,000 ft (1 minute to 2 minutes)
- From 31,000 ft to 27,000 ft: decrease of 4,000 ft (2 minutes to 3 minutes)
- From 27,000 ft to 23,000 ft: decrease of 4,000 ft (3 minutes to 4 minutes)
This suggests a linear relationship, where the altitude decreases at a constant rate.
Thus, the slope (rate of change) is -4,000 ft per minute.
To find the equation, we can use the point (1, 35,000) which corresponds to m=1 and a=35,000.
Using the slope-intercept form \( a = mx + b \):
- Here, \( m = -4,000 \)
- We need to find \( b \). Since at \( m = 1 \), \( a = 35,000 \):
\[
35,000 = -4,000(1) + b \\
35,000 = -4,000 + b \\
b = 35,000 + 4,000 = 39,000
\]
Thus, the equation for the change in altitude is:
\( a = -4,000m + 39,000 \)
Therefore, the correct answer is:
**b. \( a = -4,000m + 39,000 \)**
Given the table:
- At 1 minute, altitude = 35,000 ft
- At 2 minutes, altitude = 31,000 ft
- At 3 minutes, altitude = 27,000 ft
- At 4 minutes, altitude = 23,000 ft
We can see that the altitude decreases by 4,000 ft for each passing minute:
- From 35,000 ft to 31,000 ft: decrease of 4,000 ft (1 minute to 2 minutes)
- From 31,000 ft to 27,000 ft: decrease of 4,000 ft (2 minutes to 3 minutes)
- From 27,000 ft to 23,000 ft: decrease of 4,000 ft (3 minutes to 4 minutes)
This suggests a linear relationship, where the altitude decreases at a constant rate.
Thus, the slope (rate of change) is -4,000 ft per minute.
To find the equation, we can use the point (1, 35,000) which corresponds to m=1 and a=35,000.
Using the slope-intercept form \( a = mx + b \):
- Here, \( m = -4,000 \)
- We need to find \( b \). Since at \( m = 1 \), \( a = 35,000 \):
\[
35,000 = -4,000(1) + b \\
35,000 = -4,000 + b \\
b = 35,000 + 4,000 = 39,000
\]
Thus, the equation for the change in altitude is:
\( a = -4,000m + 39,000 \)
Therefore, the correct answer is:
**b. \( a = -4,000m + 39,000 \)**