Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 70

The relationship between Celsius and Fahrenheit temperature can be given by a linear equation. Water freezes at $0^{\circ} C$ or at $32^{\circ} F$. Water boils at $100^{\circ} C$ or at $212^{\circ} F$.

Write a linear equation expressing Fahrenheit temperature in terms of Celsius temperature.

Let $(x_1, y_1) = (0,32)$ and $(x_2, y_2) = (100,212)$ be the ordered pairs

Using the slope of the line

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{212 -32}{100-0} = \frac{180}{100} = \frac{9}{5}$

Using Point-Slope Formula


$\begin{equation} \begin{aligned} y - y_1 =& m(x - x_1) \\ \\ y - 32 =& \frac{9}{5} (x - 0) \\ \\ y - 32 =& \frac{9}{5} x \\ \\ y =& \frac{9}{5}x + 32 \\ \\ \text{or} & \\ \\ F =& \frac{9}{5}C + 32 \end{aligned} \end{equation}$