(1) one day every valley shall be exalted
(2) every hill and mountain shall be made low
(3) the rough places will be made plains
(4) the crooked places will be made straight
(5) the glory of the Lord shall be revealed
(6) all flesh shall see it together.
As clusterdude has suggested, this could have been entirely random. And "the interchangeable use of shall and will is now part of standard British and US English."
Having said that, I think that "shall" sounds a bit more epic and even ancient than "will", and that those with "shall" -- (1), (2), (5) and (6) -- are more epic or even ancient than are those with "will" -- (3) and (4). Therefore, assuming that MLK chose the words really carefully, it could have been intentional word choices on the part of MLK.
The modal verb "shall" does not mean "may", but it is a synonym for "will" and it is virtually interchangeable with "will"; however, there are slight differences in some cases and there is an old rule that still exists, particularly in England. The old rule says that the simple future looks like this:
Simple Future: I shall, you will, he will, we shall, you will, they will
Emphatic Future: I will, you shall, he shall, we will, you shall, they shall
H.W. Fowler once wrote a treatise on the differences between "shall" and "will". An example of his was that if a man yelled,
"I shall drown; no one will save me!"
he would be crying for help; in this situation, the man would be drowning and in need of being saved, whereas if a man yelled,
"I will drown; no one shall save me!"
then nobody would save the man because the man intends to die. In essence, a man who shouts this is committing suicide. That's what the difference is "technically". If your brother said about himself, "I shall be perfect for her," he was basically saying the equivalent of "I will be perfect for her." It was nothing more than his simple future prediction and he was using "I shall", which is technically more correct than "I will" in this situation, since it is a mere prediction and that's what the rules of English grammar technically call for, although it's a rule that is seldom followed. If he said to you, "You shall be perfect for her," he was basically saying, "You will be perfect for her"; however, he is being assertive about it. In essence, he was almost guaranteeing that you will be the perfect person for her.
The modal "shall" corresponds with "should" just as "will" corresponds with "would". In fact, "should" is the past tense, imperfect, and past subjunctive form of "shall" whereas "would" is the past tense, imperfect, and past subjunctive form of "will", so, essentially, you say "shall" all of the time when you say "should"; this is just its past tense, imperfect, or past subjunctive form depending upon the context wherein it may be used.
Also, grammatically-speaking, "Me and my brother were talking about a girl" is incorrect; it should say,
"My brother and I were talking about a girl."
I hope that might have helped you out. Take care and good luck.
Best Answer
Okay, "shall" and "will" are used interchangeably often, but there's a slight difference. See my post herein to read about it: What is the difference between shall and may.
As for "shall" and "should", "should" is the past tense, imperfect, and past subjunctive form of "shall", so they have several overlapping meanings. The modal shall comes from Old English sculan meaning to owe. First-person present indicative of sculan was ic sceal, meaning I shall, whereas the past indicative and past subjunctive were both ic sceolde, meaning I should.
The old future tense rule has the following paradigm:
As for your examples above, "you shall not eat" is a command, i.e. "I order you not to eat", and is much more powerful than the simple "you should not eat", which is more of a suggestion such as "you ought not to eat." In your second usage of "shall", "you shall surely die" is far more powerful than "you will surely die." If you used "will" there, it would be more of a prediction that you're going to die whereas the usage of "shall" therein is prophetic: you are like a soothsayer; you can see into the future and so you are prophesying what shall happen. The usage of "shall" almost guarantees that the event will occur.
Here are some examples below using the formal English future-tense rule:
Now, I want to reiterate that the examples above use the old future-tense rule whereon Fowler wrote his treatise in 1908. While some of the above usages still occur in English today although often inconsistently, many of them would be considered quite formal or outmoded. You should be aware of them, however, especially when you are reading the King James Bible or the English Standard Version, because this old rule is often followed in those versions of the Bible.