Interpreting Linear Relationships Quick Check

Question

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Question
A leaky bucket contains 50 ml of water and is losing water at a rate of 15 ml of water every 4 minutes. Select the graph that shows how much water will be in the bucket over time.(1 point)
Responses

A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 4 comma 35 right parenthesis, and left parenthesis 8 comma 20 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 4 comma 35 right parenthesis, and left parenthesis 8 comma 20 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 50 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 10 comma 10 right parenthesis, left parenthesis 20 comma 20 right parenthesis, and left parenthesis 30 comma 30 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 50 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 10 comma 10 right parenthesis, left parenthesis 20 comma 20 right parenthesis, and left parenthesis 30 comma 30 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 4 comma 30 right parenthesis, and left parenthesis 6 comma 40 right parenthesis. A solid arrow passes through these points.
Image with alt text: A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 4 comma 30 right parenthesis, and left parenthesis 6 comma 40 right parenthesis. A solid arrow passes through these points.

A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 40 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 20 comma 35 right parenthesis, and left parenthesis 40 comma 20 right parenthesis. A solid arrow passes through these points.

Answer 1

To determine the correct graph that represents the water level in the leaky bucket over time, we need to analyze the situation:

• The bucket initially contains 50 ml of water.
• It loses water at a rate of 15 ml every 4 minutes.

To find the rate of water loss per minute:

• Since it loses 15 ml in 4 minutes, the rate is: \[ \text{Rate} = \frac{15 \text{ ml}}{4 \text{ minutes}} = 3.75 \text{ ml/minute} \]

Now, we can calculate the amount of water left in the bucket over time:

• At \( t = 0 \) minutes, the water is 50 ml.
• At \( t = 4 \) minutes, the water will be: \[ 50 \text{ ml} - 15 \text{ ml} = 35 \text{ ml} \]
• At \( t = 8 \) minutes, the water will be: \[ 35 \text{ ml} - 15 \text{ ml} = 20 \text{ ml} \]

Now we can summarize the key points:

• (0, 50)
• (4, 35)
• (8, 20)

We are looking for a graph that plots these points.

Analyzing the options:

1. The first graph shows the points (0, 50), (4, 35), and (8, 20). This is consistent with the calculation.
2. The second graph shows different points and starts at (0, 0), which does not match our scenario.
3. The third graph starts at (0, 10), which does not match our scenario.
4. The fourth graph shows (0, 50), but the other points (20, 35) do not follow the calculated values.

Thus, the correct answer is: The first graph - it accurately represents the water level of the bucket over time with the points (0, 50), (4, 35), and (8, 20).