Example

Determine an equation that converts temperatures in degrees Fahrenheit to degrees Celsius.

Solution

Fahrenheit and Celsius temperatures are related to each other by a linear equation. Based on the well-known freezing and boiling points of water, the graph of that linear equation passes through the points $(f,c)=(32,0)$ and $(f,c)=(212,100)$. In this problem, our $x$-coordinate is described by the variable $f$, and our $y$-coordinate is described by the variable $c$.

To find the linear equation relating $f$ and $c$, we start by finding slope:

Now let's use the slope and the point $(32,0)$ to determine the point-slope form:

or