Question

A hot air balloon starts at an elevation of 200 feet above ground. It ascends, or goes up, at a constant rate of 400 feet per minute. The equation and graph below represent this situation.
What is the rate of change of this linear function? In other words, by how much does the elevation of the hot air balloon change for every additional minute?
x
y
0
1
2
3
4
5
6
7
8
9
10
0
200
400
600
800
1,000
1,200
1,400
1,600
1,800
2,000
Time in minutes
Elevation (feet)
y=400x+200

Rate of change:
Good work!
What is the initial value, or the vertical intercept, in this linear function?
x
y
0
1
2
3
4
5
6
7
8
9
10
0
200
400
600
800
1,000
1,200
1,400
1,600
1,800
2,000
Time in minutes
Elevation (feet)
y=400x+200

Rate of change: 400

Initial value:

Answer 1

The initial value, or the vertical intercept, in the linear function \( y = 400x + 200 \) is 200. This represents the initial elevation of the hot air balloon when \( x = 0 \) (at \( t = 0 \) minutes).

So, to summarize:
- **Rate of change**: 400 feet per minute
- **Initial value**: 200 feet