"A well-ordered Christian household is a powerful argument in favor of the reality of the Christian religion, —an argument that the infidel cannot gainsay. All can see that there is an influence at work in the family that affects the children, and that the God of Abraham is with them. If the homes of professed Christians had a right religious mould, they would exert a mighty influence for good. They would indeed be the “light of the world.” The God of heaven speaks to every faithful parent in the words addressed to Abraham: “I know him, that he will command his children and his household after him, and they shall keep the way of the Lord, to do justice and judgment; that the Lord may bring upon Abraham that which he hath spoken of him.” [ Genesis 18:19 .]— Patriarchs and Prophets, 143-144 . CE 222.1"
"For I know him, that he will command his children and his household after him, and they shall keep the way of the Lord, to do justice and judgment; that the Lord may bring upon Abraham that which he hath spoken of him."
Ellen White directly references Genesis 18:19 in this passage.
"Labor for the Young. —Very much has been lost to the cause of God by a lack of attention to the young. Ministers should form an acquaintance with the youth in their congregations. Many are reluctant to do this, but their neglect is a sin in the sight of Heaven. There are among us many who are not ignorant of our faith, yet whose hearts have never been touched by the power of divine grace. Can we who claim to be servants of God pass on day after day, week after week, indifferent to these souls who are out of Christ? If they should die in their sins, unwarned, their blood would be required at the unfaithful watchman's hands. CE 222.2"
"But if the watchman see the sword come, and blow not the trumpet, and the people be not warned; if the sword come, and take any person from among them, he is taken away in his iniquity; but his blood will I require at the watchman’s hand."
The EGW passage directly applies the principle of the watchman's responsibility from Ezekiel to ministers and their duty to warn and care for the youth.