To analyze the table you've provided, we'll start with the given data:
- x (time in minutes): 8, 5, 7, 2, 9
- y (distance in meters): 664, 415, 581, 166, 747
a. Every minute meters are traveled.
To find the average distance traveled per minute, we can calculate the rate of distance traveled per minute.
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First, we'll calculate the total distance traveled and the total time taken.
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Total distance traveled (y): \( 664 + 415 + 581 + 166 + 747 = 2573 \) meters
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Total time (x): \( 8 + 5 + 7 + 2 + 9 = 31 \) minutes
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Calculate the average distance per minute:
\[ \text{Average distance per minute} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2573}{31} \approx 83.3 \text{ meters per minute} \]
b. Write an equation to show the relationship between x and y:
Let’s assume a linear relationship \( y = mx + b\), where:
- m = slope (the average distance traveled per minute)
- b = y-intercept (the distance traveled when \( x = 0\))
Given our previous calculation, we can set up our equation using the average calculated slope.
Assuming there's no initial distance covered when time \( x = 0 \), we typically have \( b = 0 \) for simplification in this context. Thus, since the average distance is approximately 83.3:
\[ y = 83.3x + 0 \]
Or, simplifying:
\[ y = 83.3x \]
c. This relationship is ______ because the y-intercept is ______.
The relationship is linear because it can be expressed in the form \( y = mx + b\). The y-intercept is 0, indicating that when no time has passed (0 minutes), no distance has been traveled (0 meters).
So, filling in the blanks:
- This relationship is linear because the y-intercept is 0.
1 answer