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.
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.