Determining Min & Max Slopes w/Varying STDEV

[Salish99]

If I have a slope for which I do simple linear regression analysis, but each of the 6 datapoints of the slope have their individual (non-equal) standard deviations, how can I calculate the maximum and minimum slope of the graph?
One idea we too up was to increase the first half of the data points by the standard deviation, and decrease the other have by their standard deviations (and vice versa) in order to determine the maximum and minimum slopes from the resulting data points.
Is such an analysis valid? What else could I do to determine the maximum and minimum slopes based on the individual standard deviations?
If my explanation was unclear I have attached a document with simple made-up values for representation of the issue:
http://drop.io/stats20100/asset/minmax-gif"
This example data was created for simple commenting, the actual data is more complex.
Below the values used for this example:

x y σ, % σ y-σ y+σ MINsl MAXslope
1 1 10 0.1 0.9 1.1 1.1 0.9
2 2 20 0.4 1.6 2.4 2.4 1.6
3 3 10 0.3 2.7 3.3 3.3 2.7
4 4 10 0.4 3.6 4.4 3.6 4.4
5 5 20 1.0 4.0 6.0 4.0 6.0
6 6 10 0.6 5.4 6.6 5.4 6.6

LINEST
1 0 AVG
0.76 0.64 MIN
1.24 -0.64 MAX

 

[bpet]

each of the 6 datapoints of the slope have their individual (non-equal) standard deviations

Is "Weighted Least Squares" what you were looking for?