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}
$