Question

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:-

`F=(9/5)C+32`

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

(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?

(iii) If the temperature is 95°F, what is the temperature in Celsius?

(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, 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 1

(i) `F=(9/5)C+32`

It can be observed that points (0, 32) and (−40, −40) satisfy the given equation. Therefore, these points are the solutions of this equation.

The graph of the above equation is constructed as follows.

 

(ii) Temperature = 30°C

`F=(9/5)C+32`

`F=(9/5)30+32 = 54+32=86`

Therefore, the temperature in Fahrenheit is 86°F.

 

(iii) Temperature = 95°F

`F=(9/5)C+32`

`95=(9/5)C+32`

`63=(9/5)C`

C = 35

Therefore, the temperature in Celsius is 35°C.

 

(iv) `F=(9/5)C+32`

If C = 0°C, then

`F=(9/5)0+32`

Therefore, if C = 0°C, then F = 32°F

If F = 0°F, then

`0=(9/5)C+32`

`(9/5)C=-32`

`C=-160/9=-17.77`

Therefore, if F = 0°F, then C = −17.8°C

 

(v) `F=(9/5)C+32`

Here, F = C

`F=(9/5)F+32`

`(9/5-1)F+32=0`

`(4/5)F=-32`

   F = -40

Yes, there is a temperature, −40°, which is numerically the same in both Fahrenheit and Celsius.