v5 Luke links an independent saying of Jesus on faith with what is virtually an editorial comment. He uses the post-resurrection title for Jesus, namely, "the Lord" and the official title for the twelve, "the apostles." The nature of the request is somewhat unclear, but is usually interpreted along the line of the apostles asking for the "faith", as in the sense of spiritual strength, to forgive unconditionally, cf. v4. So προσθες ιs usually translated as "increase", ie. "bolster up our capacity to forgive." The trouble is that we end up with a strange usage of πιστις, "faith", and a rather unconvincing translation of προστιθημι, which properly takes the sense "to give, provide, grant." So, what point is Luke making? Faith is the only "yoke" to place on "the little ones." The disciples have been warned of the Pharisees self-righteous law-obedience and the danger this poses for God's "little ones." Christ's demand for unconditional forgiveness (the standard was 3 times, but for Jesus even 7 times in a day) exposes the folly of a righteousness based on works. Luke, if not a colleague of Paul, at least seems tuned to Paul's understanding of Jesus' teaching on the means of grace.
τω κυριω (ος) dat. "[said] to the Lord" - Dative of indirect object.
προσθες (προστιθημι) aor. imp. "increase" - add to. Numerous meanings are possible: "give us faith", BAGD.; "give us also faith", Creed, in the sense of "add faith to our other gifts"; "bestow upon us more faith", Creed; "give us a greater faith than we already have", Stein. Best taken as "grant us faith", Evans; see above.
ημιν dat. pro. "our [faith]" - [faith] for us. Probably best read as a dative of interest, advantage.
v6 σιναπεως (ι εως) gen. "a mustard [seed]" - [a grain] of mustard. The genitive is adjectival, attributive.
τη συκαμινω (ος) dat. "[you can say] to this mulberry tree" - Dative of indirect object.
υπηκουσεν αν aor. "it will obey [you]" - it would have obeyed [to you]. The aorist may express time before the command indicating "the certainty of (the command's) fulfilment".
v7 τις δε ..... ος ... επει (ειπον) fut. "suppose one .... Would he say ..?" - who [among you having a slave who [coming in from the field] will say? The construction is emphatic and expects the answer, "no one would ever say this to a slave." Taken as setting up a rhetorical question, which feature is lost in the complexity of the sentence, the verb to-be must be supplied; "is there anyone among you, having a slave ....... who, when he comes in from the field, will say to him ....?" Verses 8 and 9 are also best translated as rhetorical questions, TNT.
δουλον (ος) "servant" - Not really a servant, but rather "a slave", TNT.
αροτριωντα (αροτριαω) pres. part. "plowing [or looking after the sheep]" - plowing [or shepherding]. The participle, as with "shepherding", functions as the complement of the object "servant", forming an object complement double accusative (here treble) construction.
εισελθοντι (εισερχομαι) dat. aor. part. "when he comes in" - having come in. technically, standing in agreement with αυτω "him = the servant".
παρελθων (παρερχομαι) aor. part. "come along now [and sit down to eat]" - having come beside [lie down]. Attendant circumstance participle expressing action accompanying the imperatival verb "sit down." As in sitting down for a meal, although in their case, they would lie down to eat.
v8 ουχι ερει (ειπον) fut. "would he not [rather] say" - a deliberative future setting up a second rhetorical question that expects a positive answer.
ετοιμασον (ετοιμαζω) aor. imp. "prepare" δειπνησω (δειπνεω) aor. subj. fut. ind. "my supper" - probably being used to form a purpose clause, "in order that I may eat."
περιζωσαμενος (περιζωννιμι) aor. part. having wrapped about yourself - in the sense of putting on a serving apron.
διακονει (διακονεω) pres. imp. wait on "serve me until I have finished".
v9 χαριν (ις εως) "thank" gratitude due a τω δουλω (ος) dat. "the servant".
τα διαταχθεντα (διατασσω) aor. pas. part. "what he was told to do" - assigned, arranged, commanded.
v10 τα διαταχωθεντα (διατασσω) aor. pas. part. "were told to do" - the things having been commanded, instructed, assigned. The participle is adjectival, attributive, limiting παντα "all the things".
λεγετε (λεγω) pres. imp. "should say" – Actually "think" so an idiom; "you ought to remind yourself of this truth."
αχρειοι adj. "[we are] unworthy [servants]" - useless, troublesome, unprofitable. In a negative sense it may describe a slave who has done no more than was required, "we're not much good as servants as we have only done what we ought to do", or taking a positive sense, it may describe modesty, "we are servants and deserve no credit". A weaker sense, namely "unworthy", seems best. "Believers are unworthy in the sense that at their very best all they have done is what they should have done, i.e. what the commandments teach.
πεποιηκαμεν (ποιεω) perf. "we have only done" - perfect tense expressing a past act with ongoing consequences.
ποιησαι (ποιεω) aor. inf. "[our duty]" - infinitive is complementary, completing the sense of the verb "to work."