Question

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 degrees Fahrenheit at midnight and decreases 2 degrees Fahrenheit every 1/2 hour.

Answer 1

y = 60 - 4x

-4°F per hour

Explanation:

We have x hours after midnight the temperature is y. Now, the temperature is 60°F at midnight and decreases 2°F every 1/2 hours.

So, the relation between x and y can be written as y = a - bx ....... (1)

Now, at x = 0, y = 60.

Hence, a =60. {From equation (1)} and y = 60 - bx ...... (2)

Again at x =0.5, y = 60-2 = 58.

Hence, from equation (2), 58 = 60 - b(0.5), ⇒ b =
`(2)/(0.5)` = 4

Therefore, the final relation between x and y is, y = 60 - 4x ...... (3)

So, we can conclude that the relation between x and y is not proportional but linear and the unit rate of change of temperature with respect to time is -4°F per hour. (Answer)