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.

Solution:

i) F = (9/5)C + 32  ---  Equation (1)

Equation (1) represents a linear equation of the form ax + by + c = 0, where C and F are the two variables.

By substituting different values of C in equation (1), we obtain different values for F.

When C = 0, F = (9/5)C + 32 = (9/5)0 + 32 = 32

When C = - 40, F = (9/5)C + 32 = (9/5) × (- 40) + 32 = - 72 + 32 = - 40

When C = 10, F = (9/5)C + 32 = (9/5) × (10) + 32 = 18 + 32 = 50

Thus, we have the following table with all the obtained solutions:

C	0	- 40	10
F	32	- 40	50

The graph of the line represented by the given equation is shown below.

ii) Given: Temperature = 30°C

To find: F = ?

We know that, F = (9/5)C + 32

By Substituting the value of C = 30° C in the equation above,

F = (9/5)C + 32

= (9/5)30 + 32

= 54 + 32

= 86

Therefore, the temperature in Fahrenheit is 86° F .

iii) Given, Temperature = 95° F

To find, C = ?

We know that, F = (9/5)C + 32

By Substituting the value of temperature in the above equation,

95 = (9/5)C + 32

95 - 32 = (9/5)C

63 = (9/5)C

C = (63 × 5)/9

C = 35

Therefore, the temperature in Celsius is 35° C.

iv) We know that, F = (9/5)C + 32

If C = 0°, then by substituting this value in the above equation,

F = (9/5)0 + 32

F = 0 + 32

F = 32

Therefore, if C = 0°, then F = 32°

If F = 0° F, then by substituting this value in the above equation,

0 = (9/5)C + 32

(9/5)C = - 32

C = (- 32 × 5)/9

C = - 17.77

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

v) We know that, F = (9/5)C + 32

Let us consider, F = C

By Substituting this value in the equation above,

F = (9/5)C + 32

(9/5 - 1)F + 32 = 0

(4/5)F = - 32

F = (- 32 × 5)/4

Hence, F = - 40

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

☛ Check: Class 9 Maths NCERT Solutions Chapter 4

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Video Solution:

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.

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.3 Question 8:

Summary:

If the temperature is 30°C, then the temperature in Fahrenheit is 86°F. If the temperature is 95°F, then the temperature in Celsius is 35°C. If the temperature is 0°C, then the temperature in Fahrenheit is 32°F and if the temperature is 0°F, then the temperature in Celsius is 17.8°C. - 40°F is the only temperature that is numerically the same for both Fahrenheit and Celsius.

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