This passage occurs in the Revised Common Lectionary Year C, most recently September 2016.
The passage before this (17:1-4) is about forgiveness. Jesus tells his disciples to forgive people over and over. This is where they protest and ask for more faith, or "pistis". Forgiveness is hard! Faith in the Gospel of Luke is not simply "getting it" or even "getting it right" but the deep hunger for Jesus that motivates us, trees and even mountains to fall down at his feet. If you are looking for a three point sermon on faith: Faith draws us toward Jesus for forgiveness and healing; faith leads us away from Jesus in service; faith always reveals itself in humility, not in worldly greatness.
πιστις (17:5; 17:6; "faith") The word faith has taken on many theological meanings. A few comments about how Luke uses it. First, the people that have faith are always outside the circle of pious Jews and even the disciples. For example: The bleeding woman (8:48), the Samaritan leper (17:19) and the Roman Centurion (7:9). Faith leads to healing but also forgiveness (5:20, 18:42). Above all, faith leads people to move themselves toward Jesus. Faith is the motivation for people to move toward Jesus and for him to act. It is not an intellectual assent to propositions, but it is the deep, gnawing trust that moves people and moves mountains to fall at the knees of Jesus.
υμων (17:5; 17:6; "our") This is great -- the disciples ask for THEIR faith, not just my faith. Faith is a shared entity.
διακονει (17:8; to serve, minister or wait on tables). This verb is where we get the term deacon (or diaconal). It doesn't mean anything glorious, simply waiting on tables! Just a reminder though, Jesus finally says he is the one who serves us (Luke 12:37, 22:27).
αποστολοι (17:5; "apostles") Luke uses the term apostles far more than the other writers, even indicating that at the Lord's Supper (22:14) the apostles joined him. Perhaps this is because he writes Acts! I wonder if Luke helps us see that being a disciples of Jesus necessarily means being an apostle, being sent out into the world. Furthermore, the disciples/apostles in the book of Acts will do amazing things through their faith. Faith is the dynamic of moving toward Christ, seeking forgiveness and mercy and then being sent away from Christ, back into the world.
As a side note -- 17:1 begins by referring to the followers of Jesus as disciples/students (μαθητης). They are referred to as apostles in 17:5 and then servants in 17:8. Part of our calling is to learn and grow; part of our calling is to be sent; part of our calling is to serve others.
Grammar point: ει-αν clauses
When you see "εαν" this normally means there is a simple, "if (εαν) A, then B" However, if you see an ει-αν clause, this probably means that the conditions are false. This is the case in verse 6: If you had faith (which you don't), you would say (which you haven't). Great example of this construction is in John 11; "If (ει you had been here (which you weren't), my brother (αν) wouldn't have died (but he did)."
Side note: Another scholar I heard of argued that the ει was true, but that the αν statements built on each other. Ie, Since you have faith, tell the mulberry bushes (which you didn't) to up root...and they would obey (which they didn't). I don't think this is true, because John 4:10 and Matthew 24:43 have similar ει-αν-αν constructions. In both cases it is translated condition A is false, so B and C didn't happen, not A is true, B didn't happen so C didn't happen (as this scholar argues in this case).
(Warning, this sentence is complex because Luke intermixes the various components of each sentence; using Bible Works/lexicon to tell you the cases is probably essential)
BGT Luke 17:7 Τις δε εξ υμων δουλον εχων αροτριωντα η ποιμαινοντα, ος εισελθοντι εκ του αργου ερει αυτω ευθευς παρελθων αναπεσε?
NRS Luke 17:7 "Who among you would say to your slave who has just come
in from plowing or tending sheep in the field, 'Come here at once and
take your place at the table'?
Τις δε εξ υμων: Basically: Who of you? Notice the accent on the word tis leans forward? This means its a strong accent, which tells you it is a question word (who, which, what) and not an indefinite article (a, any, certain)
δουλον εχων: The verb εχων is a participle. At this point, the sentence is not too bad. For your English eyes, you probably need to switch δουλον and εχων for word order. Then you can just do the "quick sloppy circumstantial participle" translation which is where you just add "ing" to the verb. In this case, you get: "Which of you, having a slave"
αροτριωντα η ποιμαινοντα: Here is where the train wreck comes. You have another two participles. First step -- get vocab (so your brain can help you piece this together unconsciously): "plow" and "tend." Your brain probably can figure out that the slave is the one plowing and tending. How would you know for sure? Notice how these are both accusative participles? Therefore they do not refer to the subject (the one who has the slave) but the object (the slave). So the slave is under the circumstance of plowing and tending.
So, we have so far: "Which of you, having a slave, tending and plowing." Hmm...unclear in English, so we get: "Which of you, having a slave who tends and plows,"
ος εισελθοντι εκ του αργου ερει αυτω: This clause is awful because you go back and forth between subject and object. First off, your brain knows its a relative clause because you have this ος ("hos"). In fact, hos is the subject, so we need to find a normal verb to match this with. Turns out that εισελθοντι is not a normal verb, but a participle. The verb you need to find is ερει. This is a basic verb (lego, to speak) but tough to recognize in the future form. (Who will say). So we know that someone is speaking. We also know, thanks to the αυτω in the dative, that someone is speaking to someone. So, who are the someones? Well, the verb "εισελθοντι" is a participle in the dative, linked with the word αυτω . In this case it functions like an adjectival participle. Kind of strange sucker, but basically, it works like this: The one who enters from the field (εκ του αργου) is the one to whom the words will be addressed. You can know this because it all is in the dative. So you translate this relative clause like this:
"he, who will say to him, the one coming in from the field"
"will say to the one (namely the slave) coming in from the field."
One final note -- the coming in precedes the speaking (the verb is in the aorist, which in the case of participles shows order in time of events), so to make it all clear:
"will say to the slave after he has come in from the field."
Put it together and you get
"Which of you, having a slave who tends and plows, will say to the him after he comes in from the field:"
ευθεως παρελθων αναπεσε? The ευθεως means immediately...and the αναπεσε is a simple command: sit at the table.
So you have: "immediately παρελθων sit." You can translate the παρελθων (which can mean just about anything) a couple of ways. Really, it is not a key verb in the sentence; it functions more like another adverb: "immediately come over and sit." Or more politely, "Come here at once and sit!"