Question

A hot air balloon starts at an elevation of 300 feet. Then, it ascends at a rate of 600 feet per minute.
What is the slope of this line?
x
y
0
1
2
3
4
5
6
7
8
9
10
0
300
600
900
1,200
1,500
1,800
2,100
2,400
2,700
3,000
Number of minutes
Elevation in feet
The slope of this line is
.
Good work!
What does the slope mean in this situation?
x
y
0
1
2
3
4
5
6
7
8
9
10
0
300
600
900
1,200
1,500
1,800
2,100
2,400
2,700
3,000
Number of minutes
Elevation in feet
slope =
vertical distance
horizontal distance
= 600

After 600 minutes, the hot air balloon ascends 1 foot.

After each additional minute, the hot air balloon ascends 600 more feet.
Good work!
What is the vertical intercept? In other words, at what point does the line cross the vertical axis?
x
y
0
1
2
3
4
5
6
7
8
9
10
0
300
600
900
1,200
1,500
1,800
2,100
2,400
2,700
3,000
Number of minutes
Elevation in feet

Answer 1

To determine the vertical intercept (also known as the y-intercept), we look at the point where the line crosses the vertical axis (elevation in feet) when the horizontal value (number of minutes) is 0.

In this case, when the hot air balloon starts (at 0 minutes), its elevation is given as 300 feet. Therefore, the vertical intercept is:

**Vertical Intercept = 300 feet**

This means that at time \(x = 0\) (0 minutes), the balloon is at an elevation of 300 feet.