Which graph correctly represents 1/3 y - 1/2 x >2 ?

For best fit, it allows you to check the overall relationship of the data (so it can show a positive or negative correlation). So you can make predicted measurements for the future based on the overall relationship of the data.
However, with outliers it can skew your data by a little- to large amount depending on the difference from the 'majority' of the data you have.
If points are way out- the line of best fit won't be very accurate since it's just an overall average of points.
If the points are mostly together (i.e not a lot of 'crazy' outliers)- then the line of best fit is a good relationship. You can use the r^2 value to find out whether the relationship is close or not.
Hope this helps with your brainstorming :>