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:

Answer 1

The rate of change of the linear function \( y = 400x + 200 \) is represented by the coefficient of \( x \), which is 400. This means that for every additional minute (each unit increase in \( x \)), the elevation of the hot air balloon increases by 400 feet.

So, the rate of change is:

**Rate of change: 400 feet per minute**.