In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is linear equation that converts Fahrenheit to Celsius.
F = (\(\frac{9}{5} \) )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 \(30^{\circ}\)C , what is the temperature in Fahrenheit?
(iii) If the temperature is 95F , what is the temperature in Celsius?
(iv) If the temperature is \(0^{\circ}\)C , what is the temperature in Fahrenheit and if the temperature is 0F , 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.

The linear equation that converts Fahrenheit to Celsius is
F = (\(\frac{9}{5} \))C + 32
\(\Rightarrow \) 5F - 9C = 160....(i)
For plotting points, we get the following table :

C	0	-160/9	-40
F = (9/5)C + 32	32	0	-40
Points	A(0, 32)	B(-160/9, 0)	c(-40, -40)

Here, we plot the given points on graph paper and join all these points to form a line.

ii)



ii)If the temperature is \(30^{\circ}\)C i.e.,C = \(30^{\circ}\)C
Then we get,

F = (\(\frac{9}{5} \) )×(30) + 32
= 9 × 6 + 32
= 54 + 32 = 86

Therefore, the temperature in Fahrenheit is 86F


iii)If the temperature is 95F i.e.,F = 95

Then we get, from eq.(i)

5(95) - 9C = 160
\(\Rightarrow \) 9C = 475 - 160 = 315

\(\therefore \) C = \(35^{\circ}\)C.

Therefore, the temperature in Celsius is \(35^{\circ}\)C


iv)If the temperature is \(0^{\circ}\)C i.e.,C = \(0^{\circ}\)

Then we get,

F = (\(\frac{9}{5} \) )×(0) + 32 = 32

Therefore, the temperature in Fahrenheit is 32F.

If the temperature is 0F i.e.,F = 0

Then we get, from eq.(i)

5(0) - 9C = 160
\(\Rightarrow \) C = \(\frac{-160}{9} ^{\circ}\)C

Therefore, the temperature in celsius is \(\frac{-160}{9} ^{\circ}\)C.


V)For this, let us take C = F,

Thus from eq.(i) we get,

5F - 9F = 160
\(\Rightarrow \) -4F = 160
\(\Rightarrow \) F = -40
Therefore, C = F = \(-40^{\circ}\)