A hot air balloon starts at an elevation of 3000 feet above ground. It descends, or goes down, at a constant rate of 500 feet per minute. The equation and graph below represent this situation.

Question

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
250
500
750
1,000
1,250
1,500
1,750
2,000
2,250
2,500
2,750
3,000
Time in minutes
Elevation (feet)
y=−500x+3000

Rate of change:

Answer 1

The rate of change of the linear function \( y = -500x + 3000 \) represents the change in elevation of the hot air balloon per minute.

In this equation:

• The coefficient of \( x \) (which is -500) indicates how much the elevation changes for each additional minute.
• Since the rate is negative, it means that the elevation is decreasing.

Thus, the rate of change is \(-500\) feet per minute.

So, for every additional minute, the elevation of the hot air balloon decreases by 500 feet.

Rate of change: -500 feet/minute