Why was the line of best fit method used to determine the experimental value of absolute zero?

Explanation:

Charle's Law for ideal gases states that, at constant pressure, the temperature and the volume of a sample of gas are protortional.

That means that the graph of the relationship between Temperature, in Kelivn, and Volume is a line, which passes through the origin.

When you work with Temperature in Celsius, and the temperature is placed on the x-axis, the line is shifted to the left  273.15ºC.

Meaning that the Volume at 273.15ºC is zero.

You cannot reach such low temperatures in an experiment, and also, volume zero is not real.

Nevertheless, you can draw the line of best fit and extend it until the x-axis (corresponding to a theoretical volume equal to zero), and read the corresponding temperature.

Subject to the experimental errors, and the fact that the real gases are not ideal, the temperature that you read on the x-axis is the minimum possible temperature (absolute zero) as the minimum possible volume is zero.