Let's break down the problem step by step using the provided information.
Analyzing the relationship between x and y
- First, let's identify the distance traveled per minute by finding the ratio of distance to time for any of the points in the table.
- For example, if we take the first data point where x = 4 and y = 76:
- Distance per minute = 76 meters / 4 minutes = 19 meters per minute.
- This ratio will hold for the other data points as well:
- 57 meters / 3 minutes = 19 meters per minute,
- 190 meters / 10 minutes = 19 meters per minute,
- 133 meters / 7 minutes = 19 meters per minute,
- 171 meters / 9 minutes = 19 meters per minute.
Responses
Given this analysis, we can fill in the inputs:
a. Every minute 19 meters are traveled.
b. To find the equation that shows the relationship between x (time in minutes) and y (distance in meters), since we've established that the relationship is linear and based on the ratio found above:
- The equation can be derived as \( y = 19x \).
Therefore, the response is:
- y=19x.
c. Since the relationship is linear and passes through the origin (0,0) and has a constant rate of change (19) with a y-intercept at y = 0, we conclude that:
- This relationship is proportional because the y-intercept is (0,0).
Full Responses
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).