To analyze the data and answer the questions, we can follow these steps:
Given Data
- Time (x) in minutes: 8, 5, 7, 2, 9
- Distance (y) in meters: 664, 415, 581, 166, 747
a. Every minute, ___ meters are traveled.
To determine the average speed of travel in meters per minute, we can calculate the average distance traveled per minute based on the provided data.
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Calculate Total Distance and Total Time:
- Total distance \( = 664 + 415 + 581 + 166 + 747 = 2573 , \text{meters} \)
- Total time \( = 8 + 5 + 7 + 2 + 9 = 31 , \text{minutes} \)
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Average Speed (meters per minute): \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2573 , \text{meters}}{31 , \text{minutes}} \approx 83.3 , \text{meters/minute} \]
Answer: Every minute approximately 83.3 meters are traveled.
b. Write an equation to show the relationship between x and y:
To find a linear equation that models the relationship between distance (y) and time (x), we can use the form of the linear equation:
\[ y = mx + b \]
Where:
- \( m \) is the slope (average speed)
- \( b \) is the y-intercept (distance at time 0)
Using the average speed we just calculated:
- \( m \approx 83.3 \)
To calculate \( b \), we can inspect the data and see if we can derive the y-intercept. If we were to extrapolate back to \( x = 0 \) using the average speed, we can treat \( b \) as 0 for simplification in the absence of more specific rules-data.
However, to derive the exact relationship and y-intercept, we commonly perform linear regression or calculate based on existing data points. Given the nature, if we take, for simplicity, \( b = 0 \):
Thus, an approximate equation might be: \[ y = 83.3x + 0 \]
Answer: The equation is \( y = 83.3x \) (for a simple approximation). More analysis may adjust the slope and the intercept based on real data fitting.
c. This relationship is ____ because the y-intercept is ____.
- The relationship is linear (assuming a straight-line correlation).
- The y-intercept is 0 (if we assume distance starts at 0 when time is 0 in a simplest context; else calculation of \( b \) may provide a more accurate non-zero intercept).
Answer: This relationship is linear because the y-intercept is 0 (or as derived from regression fitting, needs calculation).
For more accurate results, graphical analysis or statistical regression would provide precise figures.
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