Why does the regression line pass through the mean of x and y?

[Cheman]

Why according to statisticians should a regression line (line of best fit) pass through the mean of x and mean of y? (ie - x bar and y bar) Why does this make the regression line more accurate? Thanks in advance. :-)

 

[Zurtex]

The line of best fit is the line that best fits the average of the points right? This would mean the point where it is the exact average of x and the exact average of y would be quite an obvious point on this line.