Chapter 1.3, Problem 97E

To determine

To write: linear equation that expresses the relationship between the temperature in degrees Celsius C and degrees Fahrenheit F .

Answer to Problem 97E

  $F=1.8C+32$

Explanation of Solution

Given:

Water freezes at $0°C$

  $\left(32°F\right)$ and boils at $100°C$ $\left(212°F\right)$

Concept Used:

Two-point form of equation of line:

The equation of line passing through two point

  $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ where $x_1\ne x_2$ .

Let C represents the temperature in degrees Celsius and F represents the temperature in degrees Fahrenheit.

Now it is given that for $C=0$ , $F=32$ . It can be written as $\left(0,32\right)$ .

And for $C=100$ , $F=212$ . It can be written as $\left(100,212\right)$ .

Now, to find the required equation of line use two point form of equation of line and substitute $\left(x_1,y_1\right)=\left(0,32\right)$ and $\left(x_2,y_2\right)=\left(100,212\right)$

  $\begin{array}{c}F-32=\left(\frac{212-32}{100-0}\right)\left(C-0\right)\\ F-32=\left(\frac{180}{100}\right)C\\ F-32=1.8C\\ F=1.8C+32\end{array}$

Conclusion:

The linear equation that expresses the relationship between the temperature in degrees Celsius C and degrees Fahrenheit F is $F=1.8C+32$ .