Question
Which line on the graph represents the information in the table?
Cost of Pencils
Number of Pencils
Total Cost (in $)
2
0.50
4
1.00
6
1.50
8
2.00
On a coordinate plane, the x-axis is labeled Number of pencils and the y-axis is labeled total cost in dollars. Line a goes through points (1, 4) and (2, 8). Line b goes through points (1, 2) and (2, 4). Line c goes through (2, 1) and (4, 2). Line d goes through (4, 1) and (8, 2).
line a
line b
line c
line d
Cost of Pencils
Number of Pencils
Total Cost (in $)
2
0.50
4
1.00
6
1.50
8
2.00
On a coordinate plane, the x-axis is labeled Number of pencils and the y-axis is labeled total cost in dollars. Line a goes through points (1, 4) and (2, 8). Line b goes through points (1, 2) and (2, 4). Line c goes through (2, 1) and (4, 2). Line d goes through (4, 1) and (8, 2).
line a
line b
line c
line d
Answers
Answered by
GPT-4o mini
To determine which line on the graph represents the information in the table, we need to analyze the data provided in the table which shows the relationship between the number of pencils and the total cost.
The data in the table is as follows:
- For 2 pencils, the total cost is $0.50.
- For 4 pencils, the total cost is $1.00.
- For 6 pencils, the total cost is $1.50.
- For 8 pencils, the total cost is $2.00.
Now, let's summarize the points based on the table:
- (2, 0.50)
- (4, 1.00)
- (6, 1.50)
- (8, 2.00)
Next, let's analyze the provided lines:
- **Line a**: Passes through (1, 4) and (2, 8).
- **Line b**: Passes through (1, 2) and (2, 4).
- **Line c**: Passes through (2, 1) and (4, 2).
- **Line d**: Passes through (4, 1) and (8, 2).
Now, we need to find a line that will correctly connect the points derived from the table.
Looking at the points associated with line c:
- At (2, 1) and (4, 2), the slope seems incorrect as line c does not contain the values that match our table points directly.
Checking the costs from the other lines:
- Line a and line b show a higher Y-cost,
- Line d shows points that also do not include 0.50, 1.00, etc., from the table data.
Upon reviewing carefully:
- **Line d** looks promising: Though it appears to go through two points (4, 1) to (8, 2), if we calculate the increment, it shows the same costs at greater quantities.
### Conclusion:
The line that would fit the relationship between the costs & number of items correctly is **not** listed exactly in the options because none match. The answer that indicates it goes near the closest points could be **line d** based on linearity, yet please consider the presented information; none really represent an exact fit based on cost increments of $\$0.50$ for every $2$ pencils.
To summarize, based on our analysis, **line c** above shows incorrect points directly matching. If further data shows true relations, they might need reevaluation to match more correctly actual costs vs lines.
So the answer to your question is that there may not be a perfectly correct line based only on provided info. But approximate assumptions made indicate it as **line d concludes close to show relations but independence checks matter for logical transformation**.
The data in the table is as follows:
- For 2 pencils, the total cost is $0.50.
- For 4 pencils, the total cost is $1.00.
- For 6 pencils, the total cost is $1.50.
- For 8 pencils, the total cost is $2.00.
Now, let's summarize the points based on the table:
- (2, 0.50)
- (4, 1.00)
- (6, 1.50)
- (8, 2.00)
Next, let's analyze the provided lines:
- **Line a**: Passes through (1, 4) and (2, 8).
- **Line b**: Passes through (1, 2) and (2, 4).
- **Line c**: Passes through (2, 1) and (4, 2).
- **Line d**: Passes through (4, 1) and (8, 2).
Now, we need to find a line that will correctly connect the points derived from the table.
Looking at the points associated with line c:
- At (2, 1) and (4, 2), the slope seems incorrect as line c does not contain the values that match our table points directly.
Checking the costs from the other lines:
- Line a and line b show a higher Y-cost,
- Line d shows points that also do not include 0.50, 1.00, etc., from the table data.
Upon reviewing carefully:
- **Line d** looks promising: Though it appears to go through two points (4, 1) to (8, 2), if we calculate the increment, it shows the same costs at greater quantities.
### Conclusion:
The line that would fit the relationship between the costs & number of items correctly is **not** listed exactly in the options because none match. The answer that indicates it goes near the closest points could be **line d** based on linearity, yet please consider the presented information; none really represent an exact fit based on cost increments of $\$0.50$ for every $2$ pencils.
To summarize, based on our analysis, **line c** above shows incorrect points directly matching. If further data shows true relations, they might need reevaluation to match more correctly actual costs vs lines.
So the answer to your question is that there may not be a perfectly correct line based only on provided info. But approximate assumptions made indicate it as **line d concludes close to show relations but independence checks matter for logical transformation**.
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