Watch the Week 6: Building the Minor Line online guitar lesson by Joe Pinnavaia from Guitar Soloing Essentials
The second Mode in a Major Scale is the Dorian Mode and goes real well with a Minor 7 chord. The way to practice these really is to do the ascending and then descending forms and then play the chord to really hear the minor tonality. The backing track is important as well, so work on soloing right away with just simple phrases or just play the mode against the track and keep your ears open!
The detailed reason why Dorian works so well:
It may be considered an "excerpt" of a major scale played from the pitch a whole tone above the major scale's tonic (in the key of C Major it would be D, E, F, G, A, B, C, D), i.e., a major scale played from its second scale degree up to its second degree again. The resulting scale is, however, minor (or has a minor "feel" or character) because as the "D" becomes the new tonal centre the minor third between the D and the F make us "hear minor". If we build a chord on the tonic, third and fifth, it is a minor chord.