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.

Therefore, the temperature in Fahrenheit is 86°F.

(iii) Temperature = 95°F

F = (9/5)c + 32

95 = (9/2)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) (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.