Question
A bucket is being filled with water. The graph below shows the water height (in ) versus the time the water has been running (in seconds).
Use the graph to answer the questions.
Height ()
y510152025303540x12345670
Time (seconds)
(a)
How much does the height of the water increase for each second the water is running?
(b)
What is the slope of the line?
Use the graph to answer the questions.
Height ()
y510152025303540x12345670
Time (seconds)
(a)
How much does the height of the water increase for each second the water is running?
(b)
What is the slope of the line?
Answers
GPT-4o mini
To answer your questions based on the graph you described:
(a) To determine how much the height of the water increases for each second the water is running, you need to look at the change in height (y-axis) for each unit of time (x-axis). If the values increase linearly on the graph, you can find the increase in height per second by calculating the rise over run:
Increase in height per second = Change in height / Change in time.
For instance, if the water height goes from 0 to 20 units in 4 seconds, it increases 20 units over 4 seconds, which means the increase per second is:
20 units / 4 seconds = 5 units/second.
(b) The slope of the line on the graph represents the rate of change of the height of the water with respect to time, which is equivalent to the increase in height for each second the water is running. Therefore, the slope can be calculated as described above:
Slope = Rise / Run.
Using the example values again, if the line rises 20 units over a run of 4 seconds, then the slope is 20 / 4 = 5.
In summary:
(a) The height of the water increases by \( x \) units per second (where \( x \) is the calculated increase from the graph).
(b) The slope of the line is also \( x \) (where \( x \) is the same value as in part a).
(a) To determine how much the height of the water increases for each second the water is running, you need to look at the change in height (y-axis) for each unit of time (x-axis). If the values increase linearly on the graph, you can find the increase in height per second by calculating the rise over run:
Increase in height per second = Change in height / Change in time.
For instance, if the water height goes from 0 to 20 units in 4 seconds, it increases 20 units over 4 seconds, which means the increase per second is:
20 units / 4 seconds = 5 units/second.
(b) The slope of the line on the graph represents the rate of change of the height of the water with respect to time, which is equivalent to the increase in height for each second the water is running. Therefore, the slope can be calculated as described above:
Slope = Rise / Run.
Using the example values again, if the line rises 20 units over a run of 4 seconds, then the slope is 20 / 4 = 5.
In summary:
(a) The height of the water increases by \( x \) units per second (where \( x \) is the calculated increase from the graph).
(b) The slope of the line is also \( x \) (where \( x \) is the same value as in part a).