Tell whether x and y are in a proportional relationship. If so, find the unit rate.
Let y be the temperature x hours after midnight. The temperature is 60∘F at midnight and decreases 2∘F every 12 hour.
To determine if x and y are in a proportional relationship, we need to check if y changes at a constant rate as x increases. In this case, y represents the temperature x hours after midnight.
From the information given, we know that the temperature is 60∘F at midnight (x = 0) and decreases 2∘F every 12 hours.
We can set up a table to observe the relation between x and y:
| x (hours after midnight) | y (temperature) |
|------------------------|--------------|
| 0 | 60 |
| 12 | 58 |
| 24 | 56 |
| 36 | 54 |
Looking at the table, we can see that as x increases by 12 hours, y decreases by 2∘F. This means that for every increase of 12 hours, the temperature decreases by 2∘F consistently.
Therefore, x and y are in a proportional relationship and the unit rate is 2∘F per 12 hours.