Quote 1
DUNCAN
My plenteous joys,
Wanton in fulness, seek to hide themselves
In drops of sorrow.—Sons, kinsmen, thanes,
And you whose places are the nearest, know
We will establish our estate upon
Our eldest, Malcolm, whom we name hereafter
The Prince of Cumberland; which honor must
Not unaccompanied invest him only,
But signs of nobleness, like stars, shall shine
On all deservers.—From hence to Inverness
And bind us further to you. (1.4.39-49)
When King Duncan names his son, Malcolm, the Prince of Cumberland, he's essentially naming him the heir apparent to the throne. Fun fact: he's seriously out of order here, since Scotland was an elective monarchy at the time. This is all Macbeth needs to decide that Malcolm and King Duncan are nothing but an obstacle in his path to ultimate power.
Quote 2
DUNCAN
There's no art
To find the mind's construction in the face.
He was a gentleman on whom I built
An absolute trust. (1.4.13-16)
Here, King Duncan says that the former Thane of Cawdor (who turned out to be a traitor) seemed to be a "gentleman" he could "trust"; ergo, it's impossible to know a man's mind by reading his face. Um, Duncan? Maybe you should listen to yourself and stop putting all your trust in the next treacherous Thane of Cawdor.
Quote 3
DUNCAN
See, see, our honour'd hostess!—
The love that follows us sometime is our trouble,
Which still we thank as love. […]
Fair and noble hostess,
We are your guest to-night. (1.6.13-15;30-31)
Hope you have your highlighters handy, fair Shmoopers: whenever you see the word "fair," it's a good bet you'll want to uncap them. Since we already know that "fair is foul," Duncan's attempted compliment comes with a big helping of dramatic irony.