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:
$F = \frac{9}{5} C + 32$
(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.

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:

$F = \frac{9}{5} C + 32$

(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.

Infinity Learn · Accepted Answer

(i) We have, F = 95 C + 32 For C = 0 , F = (95) x 0 + 32 = 32When C = 15, F = (95 )(-15) + 32= -27 + 32 = 5When C = -10, F =(95) (-10) +32 = -18 + 32 = 14 Plotting the points (0, 32), (-15, 5) and (-10,14) on a graph paper and joining them, we get a straight line AB. (ii) From the graph, 86°F corresponds to 30°C.(iii) From the graph, 95°F corresponds 35°C.(iv) We have, C = 0F = (95)0 + 32 = 32Also, F = 00 = (95)C + 32 ⇒ −32×59 = C ⇒ C = -17.8(v) When F = C (numerically)F = 95F + 32 ⇒ F – 95F= 32⇒ −45F = 32⇒ F = -40∴ Temperature is – 40° both in F and C.

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