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?
(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.
Solution (i)
To draw graph of
, we will find 3 or 4 set of solutions.
Putting
in the equation
, we get
Therefore,
is one of the infinite possible solutions.
Similarly, putting
in the equation
, we get
Therefore,
is one of the infinite possible solutions.
Putting
in the equation
, we get
Therefore,
is one of the infinite possible solutions.
Therefore, three different solutions for equation
are:
Now, we plot all these three points on the Cartesian plane. When we join these points, it makes a straight line.
Solution (ii)
Putting 30°C in equation,
, we get
Therefore, 30°C =86°F.
Solution (iii)
Putting 95°F in
, we get
Therefore, 95°F=35°C.
Solution (iv)
Putting 0°F in
, we get
approximately.
Therefore, 0°F is equal to -17.8°C approximately.
Similarly, putting 0°C in
, we get
Therefore, 0°C is equal to 32°F. (We can also see this in the graph shown above.)
Solution (v)
Yes, there is temperature which is numerically the same in both Fahrenheit and Celsius.
Putting
in the equation
, we get
Therefore, -40°C=-40°F.
We can also see the same thing on the graph shown above.
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