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# 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 :

C0-160/9-40
F = (9/5)C + 32320-40
PointsA(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 = $$-40^{\circ}$$