The Noahic covenant was made with the house of Noah and his offspring (Gen. 9:9). The Abrahamic covenant was made with the house Abraham and his offspring (Gen. 17). The Mosaic covenant was made with the house of
Each time God initiated a new stage in the development of his relationship with His people, he entered into covenant both with the heads of household and with their descendants. This is a very clearly established pattern.
Nor did the Old Testament scriptures give any indication that this pattern would change in the age to come. In fact, the prophets who announced beforehand the days of Messiah clearly proclaimed that God would follow this same principle when he established the New Covenant.
"And as for me, this is my covenant with them," says the LORD: "My Spirit that is upon you, and my words that I have put in your mouth, shall not depart out of your mouth, or out of the mouth of your offspring, or out of the mouth of your children's offspring," says the LORD, "from this time forth and forevermore." (Isaiah 59:21)
I will give them one heart and one way, that they may fear me forever, for their own good and the good of their children after them. I will make with them an everlasting covenant, that I will not turn away from doing good to them. And I will put the fear of me in their hearts, that they may not turn from me. (Jeremiah 32:39-40).
They shall dwell in the land that I gave to my servant Jacob, where your fathers lived. They and their children and their children's children shall dwell there forever, and David my servant shall be their prince forever. I will make a covenant of peace with them. It shall be an everlasting covenant with them. (Ezekiel 37:25-26)As he looked ahead, then, the ancient Israelite had every reason to believe that, just as God had always included children in the covenants he made in the past, so would He continue to do in the future.