To convert a temperature in degrees Celsius to degrees Fahrenheit, multiply the Celsius temperature by 9/5 and then add 32 degrees. Is a temperature in degrees Celsius proportional to its equivalent temperature in degrees Fahrenheit? Explain your reasoning.

Someone please help! I am rather baffled.

no. If it were proportional, that "add 32" could not be there.

Okay. Thanks!

I don't know! Help me

hubdubbud

To determine if a temperature in degrees Celsius is proportional to its equivalent temperature in degrees Fahrenheit, we need to compare the ratios of the temperature in Celsius to the temperature in Fahrenheit.

Let's take two arbitrary temperatures: T1 and T2 in degrees Celsius. According to the conversion formula, we can write the equivalent temperature in Fahrenheit as F(T1) = (9/5) * T1 + 32 and F(T2) = (9/5) * T2 + 32.

Now, to check for proportionality, we need to compare the ratios of F(T1) / T1 and F(T2) / T2.

Dividing both sides of the equation F(T1) = (9/5) * T1 + 32 by T1, we get:
F(T1) / T1 = [(9/5) * T1 + 32] / T1
= (9/5) + 32/T1

Similarly, dividing F(T2) = (9/5) * T2 + 32 by T2, we get:
F(T2) / T2 = [(9/5) * T2 + 32] / T2
= (9/5) + 32/T2

If these ratios F(T1) / T1 and F(T2) / T2 are equal, we can conclude that temperature in degrees Celsius is proportional to its equivalent temperature in degrees Fahrenheit.

However, let's simplify these ratios and see if they are equal:
F(T1) / T1 = (9/5) + 32/T1
F(T2) / T2 = (9/5) + 32/T2

We can observe that these ratios are not equal, unless T1 and T2 are equal. In other words, the ratio of Fahrenheit to Celsius temperature changes depending on the specific Celsius temperature. Hence, we can conclude that a temperature in degrees Celsius is not directly proportional to its equivalent temperature in degrees Fahrenheit.