1. ## writing equations

Let us pretend we do not know the conversion for Celsius to Fahrenheit. It is known that water freezes at 0 degrees C and 32 degrees F and boils at 100 degrees C and 212 degrees F. If C represents the temperature in degrees Celsius, give an expression that represents the corresponding temperature in degrees Fahrenheit.

2. Originally Posted by ihavvaquestion
Let us pretend we do not know the conversion for Celsius to Fahrenheit. It is known that water freezes at 0 degrees C and 32 degrees F and boils at 100 degrees C and 212 degrees F. If C represents the temperature in degrees Celsius, give an expression that represents the corresponding temperature in degrees Fahrenheit.
Hi ihavvaquestion,

firstly, you'd need to know whether or not the conversion is linear or non-linear.

For temperature conversion, both linear scales,
we have a linear relationship.

As the Fahrenheit temperatures are higher,
we will use the y=mx+c linear conversion

$\displaystyle y=mx+c\ \Rightarrow\ F=kC+F_0$

As 0 Celsius is 32 Fahrenheit...

$\displaystyle F=kC+32$

Using 212 F = 100 C, we find k

$\displaystyle 212=100k+32$

$\displaystyle 212-32=100k$

$\displaystyle 180=100k$

$\displaystyle k=\frac{180}{100}=1.8$

$\displaystyle F=1.8C+32$