To analyze the relationship between time (x) and distance traveled (y) based on the provided data, we'll go through each part of the question step by step.
Given data:
- x (time in minutes): 8, 5, 7, 2, 9
- y (distance traveled in meters): 664, 415, 581, 166, 747
a. Every minute ____ meters are traveled.
To find the average meters traveled per minute, we can calculate the ratio of distance to time for each pair and then find the average:
- For (8, 664): \( \frac{664}{8} = 83\)
- For (5, 415): \( \frac{415}{5} = 83\)
- For (7, 581): \( \frac{581}{7} \approx 83\) (exactly 83.86, but we take the average)
- For (2, 166): \( \frac{166}{2} = 83\)
- For (9, 747): \( \frac{747}{9} \approx 83\) (exactly 83, as it's 83.0)
This suggests that every minute approximately 83 meters are traveled.
b. Write an equation to show the relationship between x and y:
Since we determined the average meters per minute is 83, we can express the relationship (assuming this is linear) as:
\( y = 83x \)
c. This relationship is ____ because the y-intercept is ____.
Now, let's determine if the relationship is proportional or non-proportional:
- A linear relationship of the form \(y = mx + b\) is proportional if \(b = 0\) (the y-intercept is 0). If there is a non-zero y-intercept (b ≠ 0), it is non-proportional.
In our case, \( y = 83x \) has a y-intercept of \(0\) (which means when \(x = 0, y = 0\)), indicating a proportional relationship.
Therefore, the answers are as follows:
- a. Every minute 83 meters are traveled.
- b. Write an equation: \( y = 83x \)
- c. This relationship is proportional because the y-intercept is (0,0).
So the completed answers are: a. 83 b. y = 83x c. proportional; y-intercept is (0,0).
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