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:

(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)

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

Therefore, the temperature in Fahrenheit is 86°F.

(iii) Temperature = 95°F

Therefore, the temperature in Celsius is 35°C.

(iv)

If C = 0°C, then

Therefore, if C = 0°C, then F = 32°F

If F = 0°F, then

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

(v)

Here, F = C

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