Least-squares regression line

[Harry_the_cat]

The least-squares regression line (of y on x) minimises the sum of the squares of the vertical distances between the data points and the line.
I am trying to explain to a person (with no calculus background) why this is not the same as minimising just the sum of the vertical distances (ie without squaring them).
Any ideas how I can convince them that these are not the same, and in general will lead to two different lines, without using calculus in the explanation.

 

[Steven G]

You can have wide spread, but the sum can still be 0 if you don't square. This does not mean the points lie on the line as it would be if you squared the difference. Also let the sum just be near 0 but again with wide spreads.