In construction, the plumb line tests whether what was erected is perpendicular to the square, that is, if it is straight up and down, if it is upright. It provides a standard against which one can measure what he has built. Metaphorically, when God draws near with the plumb line, He is looking for those people who are living and abiding in His grace and His law. The Israelites' moral standards had degenerated, so their religious profession was not verified by the right kind of works. They were not upright; they failed the test.
Amos has no opportunity to intercede at this point. God will no longer relent. "I will not pass by them anymore" means that God would not overlook their sins any longer. And, if He will not pass by them, He must pass through them. The plumb line shows that He will pass through "with the sword" in judgment; His patience and forgiveness have finally ended. He could no longer defer the punishment for their sins—the time had come to destroy them.
God passes through by destroying "the high places of Isaac," the altars and idols of the false religions responsible for the moral, spiritual, and ethical decline of the people. They worshipped Baal and a host of other foreign deities (Judges 10:6). They set up sacred pillars and idols throughout the land (I Kings 14:23; II Kings 17:10-13). Some of them even burned their sons in the fire to Molech (Ezekiel 16:20-21). Through their spiritual harlotry, they abused grace—the free, unmerited pardon of God—and rejected His law.
"The sanctuaries of Israel," the religious shrines of Bethel, Dan, Gilgal, and Beersheba, would also be among the first to fall. They were the fountainheads of the attitudes of the nation. In them the people were taught to seek the material prosperity that characterized the nation, and in part they sought this physical abundance through cultic fornication and fertility rituals done in the name of the eternal God. The religions taught the people how to sin and do it religiously.
Next, "the house of Jeroboam" would fall through war. Amos refers to Jeroboam I, after whom Jeroboam II was named, and worse, after whom he followed in his sins. God selected Jeroboam I to become king of the northern ten tribes of Israel after Solomon (I Kings 11:29-31), however He made the continuance of Jeroboam's dynasty contingent upon his obedience (verse 38).
But Jeroboam did not trust God. He thought that the religious festivals and sacrifices would entice Israel to return to David's line in Judah (I Kings 12:25-27). To counter that possibility, he set up counterfeit shrines in Bethel and Dan and changed the Feast of Tabernacles from the seventh month to the eighth (I Kings 12:27-33). Jeroboam turned away from the law of God, causing the people to sin.
Historians examine economics, social conditions, and military strength to determine what causes the rise or fall of nations, but God shows that His purpose and the morality of the people are the true causes. Thus, God makes sure that the two major motivators of Israel's spiritual decline, the religious and political leadership, would feel His wrath first (Isaiah 9:13-16).