The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation, c= 5F-160 9 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?

c= 5F-160 9 putting C = 0^ , we get 0= 5F-160 9 0=5F-160 5F=160 =160 5 =32^ Now, putting F = 0^ , we get C= 5F-160 9 =5(0)-160 9 = (-160 9 )^ If the temperature in Fahrenheit is 32^ and if the temperature is 0^ F, then the temperature in Celsius is (-160 9 )^ .

The linear equation that converts Fahrenheit (F) to Celsius (C) i…

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Question

The linear equation that converts Fahrenheit $(F)$ to Celsius $(C)$ is given by the relation,
$\text{c}=\frac{5\text{F}-160}{9}$
If the temperature is $0^\circ C$, what is the temperature in Fahrenheit and if the temperature is $0^\circ F$, what is the temperature in Celsius?

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Answer

$\text{c}=\frac{5\text{F}-160}{9}$
putting $C = 0^\circ $, we get
$0=\frac{5\text{F}-160}{9}\Rightarrow0=5\text{F}-160$
$\Rightarrow5\text{F}=160$
$\therefore\text{F}=\frac{160}{5}=32^\circ$
Now, putting $F = 0^\circ $,
we get $\text{C}=\frac{5\text{F}-160}{9}\Rightarrow\text{C}=\frac{5(0)-160}{9}=\Big(-\frac{160}{9}\Big)^\circ$
If the temperature in Fahrenheit is $32^\circ $ and if the temperature is $0^\circ F$, then the temperature in Celsius is $\Big(-\frac{160}{9}\Big)^\circ\text{C.}$