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.
(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.