Let's analyze the problem step by step based on the given data about time (x) and distance (y).
Based on the points you provided:
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Calculating the relationship between x (time) and y (distance):
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To find how many meters are traveled per minute, we can calculate the slope (rate of change) using any two points.
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If we take two points from the table, let's say (4, 76) and (3, 57): \[ \text{slope} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{57 - 76}{3 - 4} = \frac{-19}{-1} = 19 \] This means that every minute, 19 meters are traveled.
Answer a: Every minute 19 meters are traveled.
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Writing the equation to show the relationship between x and y:
- Since we have determined that the rate is 19 meters per minute, we can express this linear relationship as: \[ y = 19x \] This means the distance is equal to 19 times the time in minutes.
Answer b: Write an equation to show the relationship between x and y: y = 19x.
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Identifying the nature of the relationship:
- Since the relationship can be expressed as \(y = 19x\), it shows that there is a direct linear relationship through the origin (0,0).
- The y-intercept in this case is 0, confirming that when there is no time, there is no distance traveled.
Answer c: This relationship is proportional because the y-intercept is (0, 0).
So, putting it all together:
a. Every minute 19 meters are traveled.
b. Write an equation to show the relationship between x and y: y = 19x.
c. This relationship is proportional because the y-intercept is (0, 0).