I think you need to get back to your client for more information.
It looks like the instrument is measuring something and doing a linear regression which fits a slope and an intercept. See
http://sv.wikipedia.org/wiki/Multipel_linjär_regressionBut "instrument slope" really means nothing in itself. It could be a shorthand for "the slope of the fitted line for Var1 vs Var2" but, for that to make any sense, one needs to know what Var1 and Var2 are.
Without more context, only a literal translation can be done.
P.S. Slope of a network is even less understandable - one could imagine Neural Networks but hardly in a Quality Testing situation.