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:
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
(i) F = (9/5)C + 32
When C = 0 then F = 32
also, when C = -10 then F = 14
| C | 0 | -10 |
| F | 32 | 14 |
(ii) Putting the value of C = 30 in F = (9/5)C + 32, we get
F = (9/5)×30 + 32
⇒ F = 54 + 32
⇒ F = 86
(iii) Putting the value of F = 95 in F = (9/5)C + 32, we get
95 = (9/5)C + 32
⇒ (9/5)C = 95 - 32
⇒ C = 63 × 5/9
⇒ C = 35
(iv) Putting the value of F = 0 in F = (9/5)C + 32, we get
0 = (9/5)C + 32
⇒ (9/5)C = -32
⇒ C = -32 × 5/9
⇒ C = -160/9
Putting the value of C = 0 in F = (9/5)C + 32, we get
F = (9/5)× 0 + 32
⇒ F = 32
(v) Here, we have to find when F = C.
Therefore, Putting F = C in F = (9/5)C + 32, we get
F = (9/5)F + 32
⇒ F - 9/5 F = 32
⇒ -4/5 F = 32
⇒ F = -40
Therefore at -40, both Fahrenheit and Celsius numerically the same.
