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:
(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?

Answer 1

Answer:

Given equation is

F = (9/5)C + 32 ....................1

We have to take Celsius for x-axis and Fahrenheit for y-axis.

Now put C = 0 in equation1, we get

F = (9/5)*0 + 32

=> F = 32

Again put C = 5 in equation1, we get

F = (9/5)*5 + 32

=> F = 9 + 32

=> F = 41

Again put C = -5 in equation1, we get

F = (9/5)*(-5) + 32

=> F = -9 + 32

=> F = 23

So

C: 0 5 -5

F: 32 41 23

Graph

When C = 30, the from equation 1

F = (9/5)*30 + 32

=> F = 9*6 + 32

=> F = 54 + 32

=> F = 86

When F = 95, the from equation 1

95 = (9/5)*C + 32

=> (9/5)*C = 95 - 32

=> (9/5)*C = 63

=> C = (63*5)/9

=> C = 7*5

=> C = 35

When C = 0, the from equation 1

F = (9/5)*0 + 32

=> F = 32

When F = 0, the from equation 1

0 = (9/5)*C + 32

=> (9/5)*C = - 32

=> C = (-32*5)/9

=> C = - 160/9

=> C = - 17.8

Let X degree of celcius = X degree of Fahrenheit, then from eqaution 1, we get

X = (9/5)*X + 32

=> X - 32 = (9/5)*X

=> 5(X - 32) = 9X

=> 5X - 160 = 9X

=> 9X - 5X = -160

=> 4X = -160

=> X = -160/4

=> X = -40

So at X = -40, both Celsius and Fahrenheit are same.