Deriving an equation relating the Fahrenheit and Celsius temperature scales

Here, our goal was to come up with an equation that relates the Fahrenheit and Celsius temperature scales.

First we picked two points that corresponded to each other. We know the temperatures at which water freezes and boils in degrees Fahrenheit and degrees Celsius. Water freezes at 32 degrees Fahrenheit or 0 degrees Celsius and boils at 212 degrees Fahrenheit or 100 degrees Celsius. We plotted the two points (0,32) and (100,212). We then found the equation of the line as shown in the picture.