Q. 84.3( 209 Votes )

In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:



(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.

(ii) If the temperature is 300C, what is the temperature in Fahrenheit?

(iii) If the temperature is 950F, what is the temperature in Celsius?

(iv) If the temperature is 00C, what is the temperature in Fahrenheit and if the temperature is 00F, what is the temperature in Celsius?

(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Answer :

(i) Given:
 

When C = 0 then F = 32,

And

When C = -10 then
F = 9(-2) + 32
  = - 18 + 32 
= 14

Now plotting the two points (0, 32) and (-10, 14)


(ii) Putting the value of C = 30 in F = () C + 32, we get


F = × 30 + 32

F = 54 + 32

F = 86

(iii) Putting the value of F = 95 in F = ()C + 32, we get


95 = ()C + 32


()C = 95 - 32


C = 63 × 


C = 35


(iv) After putting the value of F = 0 in


F = () C + 32,


We get:


0 = () C + 32


() = -32


C = -32 × 5/9


C =


Putting the value of C = 0 in


F = () C + 32,


We get:


F = () × 0 + 32


F = 32


(v) We have to find when F = C


Hence,


After putting F = C in


F = ()C + 32,


We get:


F = ()F + 32


F –  ×F = 32


F = 32


F = – 40


Therefore at value -40,


Fahrenheit and Celsius both are numerically the same.

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