Question
The table shoes Jose's rate of bicycle riding.
Minutes 5 10 15
Blocks 8 16 24
(1 point)
Line
on the graph matches the proportional relationship represented in the table.
Minutes 5 10 15
Blocks 8 16 24
(1 point)
Line
on the graph matches the proportional relationship represented in the table.
Answers
GPT-4o mini
To analyze the proportional relationship between the minutes and blocks in the table, we need to determine the rate of blocks per minute.
From the table:
- 5 minutes correspond to 8 blocks.
- 10 minutes correspond to 16 blocks.
- 15 minutes correspond to 24 blocks.
Now, we can find the ratio of blocks per minute:
1. For 5 minutes: \( \frac{8 \text{ blocks}}{5 \text{ minutes}} = 1.6 \text{ blocks per minute} \)
2. For 10 minutes: \( \frac{16 \text{ blocks}}{10 \text{ minutes}} = 1.6 \text{ blocks per minute} \)
3. For 15 minutes: \( \frac{24 \text{ blocks}}{15 \text{ minutes}} = 1.6 \text{ blocks per minute} \)
Since the ratio is consistent at 1.6 blocks per minute for all three intervals, we can conclude that there is a proportional relationship.
To illustrate this on a graph:
- The x-axis will represent "Minutes".
- The y-axis will represent "Blocks".
The points that correspond to the data from the table are (5, 8), (10, 16), and (15, 24). When plotted, these points will lie on a straight line that passes through the origin (0,0), confirming that the relationship is proportional.
The equation representing the proportional relationship is:
\[ \text{Blocks} = 1.6 \times \text{Minutes} \]
A line that matches this relationship is a straight line starting from the origin (0,0) and rising with a slope of 1.6. This line would depict the consistent increase of blocks over the minutes spent riding.
From the table:
- 5 minutes correspond to 8 blocks.
- 10 minutes correspond to 16 blocks.
- 15 minutes correspond to 24 blocks.
Now, we can find the ratio of blocks per minute:
1. For 5 minutes: \( \frac{8 \text{ blocks}}{5 \text{ minutes}} = 1.6 \text{ blocks per minute} \)
2. For 10 minutes: \( \frac{16 \text{ blocks}}{10 \text{ minutes}} = 1.6 \text{ blocks per minute} \)
3. For 15 minutes: \( \frac{24 \text{ blocks}}{15 \text{ minutes}} = 1.6 \text{ blocks per minute} \)
Since the ratio is consistent at 1.6 blocks per minute for all three intervals, we can conclude that there is a proportional relationship.
To illustrate this on a graph:
- The x-axis will represent "Minutes".
- The y-axis will represent "Blocks".
The points that correspond to the data from the table are (5, 8), (10, 16), and (15, 24). When plotted, these points will lie on a straight line that passes through the origin (0,0), confirming that the relationship is proportional.
The equation representing the proportional relationship is:
\[ \text{Blocks} = 1.6 \times \text{Minutes} \]
A line that matches this relationship is a straight line starting from the origin (0,0) and rising with a slope of 1.6. This line would depict the consistent increase of blocks over the minutes spent riding.