Elasticity of Supply

I was researching the Laffer Curve when I began to wonder about the elasticity of the supply for labor and the shape of the Laffer Curve. 

I usually use a mid-point formula but this time I wanted an exact supply elasticity formula.  Robert Frank uses 1/slope times the ratio of Price to Quantity for the point formula.  This makes a lot of sense to me because of the comparision between the x and y axis.  But why does this formula work? The formula is Price divided by (Price minus the vertical intercept).  As you can see from points A through D on the supply curve, the elasticities are the same as Mr. Frank's.  This formula only uses the y axis.  I'm dumfounded.