Question

The equation F=95C+32 relates temperature measured in degrees Celsius, C, to degrees Fahrenheit, F.

Determine whether there is a proportional relationship between C and F. Explain or show your reasoning.

Answer 1

Answer:

No, a Celsius temperature is not proportional to its equivalent Fahrenheit temperature.

Explanation:

The formula is

F=(9/5) C+ 32

F increases as C increases and F decreases as C decreases, but the relation is not a direct proportionality.

In mathematics, a direct proportion has the form

y=mx

where m is a constant.

If the formula had been F=(9/5) C, it would have been a direct proportion.

However, the addition of the + 32 term makes the formula no longer a direct proportion

Answer 2

Given : The equation F=9/5C+32 relates temperature measured in degrees Celsius, , to degrees Fahrenheit, .

To Find : Whether there is a proportional relationship between  

Solution:

proportional relationships

y ∝ x

=> y = kx    

Comparing with line line of equation

y = mx + c

m = k  , c = 0

 Hence graph of a proportional relationship must pa ss through (0, 0)

F=9/5C+ 32

C = 0

=> F = 32

Hence Does not pa ss through ( 0 ,0)

so The equation F=9/5C+32 is not a proportional relationship but a linear relationship

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