NCERT Class 9 Solutions: Linear Equation in Two Variable (Chapter 4) Exercise 4.3 – Part 6

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Common Fahrenheit to Celcius conversions

Conversion From C to F

Common Fahrenheit to Celcius conversions

Q-8 In countries like the 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.

  1. Draw the graph of the linear equation above using Celsius for and Fahrenheit for

  2. If the temperature is , what is the temperature in Fahrenheit?

  3. If the temperature is , what is the temperature in Celsius?

  4. If the temperature is , what is the temperature in Fahrenheit and if the temperature is , what is the temperature in Celsius?

  5. Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Solution:

Given equation is

  1. Draw the graph of the linear equation above using Celsius for and Fahrenheit for

    Let temperature in Celsius be and Fahrenheit be

    So the equation will be . Note how this equation expresses temperature in Fahrenheit for a given temperature in Celsius.

    To graph this equation we find a few points:

    • Putting the value of in equation (1)

      Or ,

      So the point is

    • Putting the value in equation (1)

      Or,

      So, point is

    • Putting the value in equation (1)

      Or,

      So, solution is

    Therefore graph becomes

    Graph of a line y=(9/5)x+32

    Line Describing Relation Between Celsius and Fahrenhit

    Graph of a line y=(9/5)x+32

  2. If the temperature is , what is the temperature in Fahrenheit?

    If,

  3. If the temperature is , what is the temperature in Celsius?

    So,

    Or

    Or

    Or

  4. If the temperature is , what is the temperature in Fahrenheit and if the temperature is , what is the temperature in Celsius?

    • When ,

    • When ,

      So, required temperature

  5. Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

    Let the same temperature be numerically. This temperature m in Fahrenheit should be same as temperature m in Celsius, i.e. = . We know that . Therefore,

Let’s solve this equation,

So, numerical value of required temperature