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.
(i) According to the question,
F = (9/5)C + 32
Solving the equation,
We get,
When C = 0, F = 32
When C = -10 , F = 14
The points to be plotted are (0, 32), (-10, 14)
(ii) When C = 30,
F = (9/5)C +32
F = (9×30)/5+32
= (9×6)+32
= 54+32
= 86oF
(iii) When F = 95,
95 = (9/5)C +32
(9/5)C = 95-32
(9/5)C =63
C = (63×5)/9
=35oC
(iv) When C = 0,
F = (9/5)C +32
F = (9×0)/5 +32
=0+32
=32oF
When F = 0,
0 = (9/5)C+32
(9/5)C = 0-32
(9/5)C = -32
C = (-32×5)/9
=-17.7777
=-17.8oC
(v) When F = C,
C = (9/5)C+32
C – (9/5)C = 32
(5-9)C/5 =32
(-4/5)C = 32
(-4/5)C = (-32×5)/4
= – 40oC
Hence, -40o is the temperature which is numerically the same in both Fahrenheit and Celsius.