To determine the constant of proportionality and the equation that models the relationship between distance (d) and time (t), we need to know the values from the table you have mentioned. However, I will provide guidance based on common scenarios.
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Determining the constant of proportionality: If the distance John ran (d) is directly proportional to the time he spent running (t), we can express this as: \[ d = kt \] where \( k \) is the constant of proportionality (miles per minute).
To find \( k \), divide the distance by the time (d/t) using any values from your table.
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Selecting the correct equation: You have the following options:
- \( t = 12.5d \) (This implies time is dependent on distance)
- \( d = 12.5t \) (This implies distance is 12.5 times the time)
- \( d = 0.08t \) (This implies distance is 0.08 times the time)
- \( t = d + 57.5 \) (This does not represent direct proportionality)
If you have determined that the constant of proportionality \( k \) is, for example, 12.5, then the equation would be: \[ d = 12.5t \] If \( k \) was determined to be 0.08, then it would be: \[ d = 0.08t \] However, \( t = 12.5d \) and \( t = d + 57.5 \) do not express a direct relationship.
Please provide the values from the table, or let me know what constant you have found, so I can give you the exact answers!