What does the slope of 5 represent in this situation?

Question

x
y
(3, 100)(7, 120)
0
1
2
3
4
5
6
7
8
9
10
0
20
40
60
80
100
120
140
160
180
200
Time (minutes)
Amount of Water (liters)
y= mx + b
Slope = 5

There are initially 5 liters in the tank when Matt starts filling it.

The amount of water increases 1 liter for every 5 minutes.

The amount of water increases 5 liters for each minute.

Answer 1

In the given scenario with the data points (3, 100) and (7, 120), the slope of 5 represents the rate of change of the amount of water in the tank with respect to time. To clarify each option:

1. There are initially 5 liters in the tank when Matt starts filling it. - This is likely referring to the y-intercept (b) of the line, not the slope.

2. The amount of water increases 1 liter for every 5 minutes. - This would imply a much smaller slope, not 5.

3. The amount of water increases 5 liters for each minute. - This accurately describes the meaning of the slope of 5. It indicates that for every minute that passes, the amount of water in the tank increases by 5 liters.

Therefore, the correct interpretation of the slope of 5 in this situation is that the amount of water increases 5 liters for each minute.