How do Trinitarians interpret Jesus's statement that "I live because of the Father"?

How do Christians interpret this statement by Jesus?

He means what he says - except for the Father, Jesus would still be dead.

There are several ways in which Jesus received life from the Father. Each is relevant to the enquiry.

1. Even though he never sinned and was legally set apart from the death penalty of sinners, he could not and did not raise himself from death after his crucifixion.

Rom 6:4 Christ was raised from the dead through the glory of the Father (also Gal 1:1)

John 10:18 No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again

This authority he received from his Father.

2. Jesus prayed to the Father to save him from death - not death on the cross, but the life he would forfeit at his resurrection - if he sinned once while in the flesh.

Heb 5:7 During the days of Jesus’ earthly life, He offered up prayers and petitions with loud cries and tears to the One who could save Him from death

3. Jesus was mortal in the flesh - he became immortal when raised (probably when he died, legally speaking). The Father raised him to new spirit life.

For Christ... having been put to death in the flesh, but made alive in the spirit 1 Pet 3:19

Rom 6:9 Christ, having been raised from the dead, is never to die again; death no longer is master over Him

4. When he was born of Mary, it was because of the Father through His spirit Luke 1:35

5. He has life in himself - just as the Father does and always did. This speaks of his immortal life that he was raised into.

John 5:26 For as the Father has life in Himself, so also He has granted the Son to have life in Himself.

Finally, John 6:57. Jesus explains how he now lives because of the Father, and we live in him!

Only the Father has true life - He gave it to Jesus and through him, we have it too.

Now this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent. John 17:3

If we take the statement at face value, we must understand that all human life begins in:

Genesis 1:27 KJV So God created man in his own image, in the image of God created he him; male and female created he them. 

and,

Genesis 2:7 KJV And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.

What we learn from these two Scriptures is first that God created us in his own image. So what does it mean to be created in his image.

1. John 4:24 KJV God is a Spirit: and they that worship him must worship him in spirit and in truth. 

Since God is Spirit we also must have a Spiritual component otherwise we would be unable to worship him in Spirit.

2. Genesis 1:27 KJV So God created man in his own image, in the image of God created he him; male and female created he them. 

God is trinitarian; if we are made in his image, then we must also be trinitarian. Thus we are body, Spirit and soul. God created our physical bodies from the dust of the Earth, and by breathing into that body life; (since God's life is eternal his breath of life must also be eternal), and thus man became a living Soul.

There is a small and insignificant difference difference between our physical bodies and the body of Jesus, in that our physical bodies are perishable while his is not.

Luke 24:1 through 8 KJV Now upon the first day of the week, very early in the morning, they came unto the sepulchre, bringing the spices which they had prepared, and certain others with them. And they found the stone rolled away from the sepulchre. And they entered in, and found not the body of the Lord Jesus. And it came to pass, as they were much perplexed thereabout, behold, two men stood by them in shining garments: And as they were afraid, and bowed down their faces to the earth, they said unto them, Why seek ye the living among the dead? He is not here, but is risen: remember how he spake unto you when he was yet in Galilee,   Saying, The Son of man must be delivered into the hands of sinful men, and be crucified, and the third day rise again. And they remembered his words,

Since Jesus retains his earthly body; we to must maintain a physical body of some sort, Since we are to remain in the image of God throughout eternity and so: 

1st John 3:2 KJV Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.

Since Many saw Jesus physical body ascend to His Father in Heaven, when He returns; as they saw him arise; He had a physical body. If we are to be like him, we of necessity will also have a physical body. Even though we do not know what we will be like we are assured that we will have a resurrection body, Spirit and eternal soul.

Regardless of how any particular Denomination may interpret these Scriptures they need no interpretation, in my humble opinion.

Hope this helps.

For as the Father has life in himself, so he has granted the Son also to have life in himself. - John 5:26

This Scripture is not explaining how Jesus the incarnation of the Word derives his life in a physical body. Of course all living things have God as the source of their life and without God nothing would live.

These all look to you, to give them their food in due season. When you give it to them, they gather it up; when you open your hand, they are filled with good things.  When you hide your face, they are dismayed; when you take away their breath, they die and return to their dust. When you send forth your Spirit, they are created, and you renew the face of the ground. - Psalm 104:27-30

But Jesus is revealing here that the same kind of life that the Father has in Himself, eternal self-existent life, has been granted also for the Son to have in Himself. As the Father does not need to draw upon an external source in order for Him to perpetuate His own life, so it is with the Son and so it always has been.

In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made. In him was life, and the life was the light of men. - John 1:1-4

And as the Father can choose to be the external source of life for whomever He chooses, so also the Son can give life to whomever He chooses.

For as the Father raises the dead and gives them life, so also the Son gives life to whom he will. - John 5:21

Just as the living Father sent me and I live because of the Father, so the one who feeds on me will live because of me. - John 6:57

It has always been this way. The Triune God created all things and all life is sourced in Him; both temporal life and eternal life. Nothing temporal has been created without the Son (John 1:3) and no eternal life is possible without the Son.

And this is the testimony, that God gave us eternal life, and this life is in his Son. Whoever has the Son has life; whoever does not have the Son of God does not have life. - 1 John 5:11-12

The Word (logos) that was made into flesh is the Divine Mind, not just the Word but the thought and intent behind the Word. As it is impossible to conceive of the Divine Mind existing apart from the Divine Being, so it is impossible to conceive of the Son existing apart from the Father. As it is impossible to conceive of the Divine Being apart from the Divine Mind (a mindless God), so it is impossible to conceive of the Father without the Son.

There is much confusion reconciling the Trinity with the Son's subordinate role to the Father and it is cleared up in this way. There is no ontological difference between the infinite, eternal mind of an infinite, eternal being and the infinite, eternal being itself if that being has perfect integrity. The thought (Logos) always proceeds from the being and never the being from the thought. The Divine Mind is subordinate in role but not less than ontologically.

The early church writers were accurate when they described the Son as eternally begotten of the Father. Jesus lives because of the Father but, as He is the incarnation of the eternal, infinite Divine Mind, He is not less than.

Orthodox Trinitarians believe that the Son and the Spirit are eternally dependant on the Father, just as the heat and light of the fire are distinct from one another, contemporaneous with, yet dependant on, the fire. Just as the light can say "I live because of the fire" the Son can say "I live because of the Father." Yet there is no fire without the heat or light — no Father without the Son, nor vice versa.

If this weren't true, whence would the Son derive His life? If He derived it elsewhere, He would be another God from the Father, having life apart from the Father. Which cannot be and which contradicts His express teaching.