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

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.

F=(95)C+32

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

  2. If the temperature is 30°C , what is the temperature in Fahrenheit?

  3. If the temperature is 95°F , what is the temperature in Celsius?

  4. 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?

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

Solution:

Given equation is

F=(95)C+32

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

    Let temperature in Celsius be x and Fahrenheit be y

    So the equation will be y=(95)x+32 . 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 x=0 in equation (1)

      Or , y=95×0+32=0+32=32

      So the point is (0,32)

    • Putting the value x=5 in equation (1)

      Or, y=(95)×5+32=9+32=41

      So, point is (5,41)

    • Putting the value x=5 in equation (1)

      Or, y=(95)×(5)+32=9+32=23

      So, solution is (5,23)

    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 30°C , what is the temperature in Fahrenheit?

    If, x=30°C y=(95)×30+32=54+32=85°F

  3. If the temperature is 95°F , what is the temperature in Celsius?

    So, y=95°C

    95=95×x+32

    Or 9532=95x

    Or 63=95x

    Or C=63×59=35°F

  4. 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?

    • When x=0 , y=95×0+32=0+32=32°F

    • When x=0°F , 0=(95)x+32

      (95)x=32

      x=(32×5)9=1609

      So, required temperature =160°9C

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

    y=(95)x+32

    Let the same temperature be m numerically. This temperature m in Fahrenheit should be same as temperature m in Celsius, i.e. m°F = m°C . We know that m°F=(95)m°C+32=m°C . Therefore,

Let’s solve this equation, m=95m+32

95mm=32

9m5m5=32

4m5=32

4m=32×5

m=32×54

m=8×5

m=40

So, numerical value of required temperature =40°F=40°C

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