Excellent and concise summary by John Stott from Urbana 1964 as to why accepting Jesus means accepting the authority of both the Old and New Testaments.
The Christian is under both instruction
He looks to Jesus as his Teacher to instruct him,
and as his Lord to command him.
He believes what he believes
because Jesus taught it,
and he does what he does
because Jesus said to do it.
He is our Teacher to instruct us,
and we learn to submit
and to subordinate,
our minds to his mind.
We do not presume to have views or ideas or opinions
which are in contradiction to the views and ideas
of Jesus Christ.
Our view of Scripture
is derived from Christ's view of Scripture,
just as our view of discipleship,
of heaven and hell,
of the Christian life,
and of everything else,
is derived from Jesus Christ.
Any question about the inspiration of Scripture
and its authority
therefore resolves itself to:
"What did Jesus Christ teach about these points?"
We would say,
without any doubt,
that he gave reverent assent to the authority and
inspiration of the Old Testament.
There is no indication anywhere in his teachings
that he disagreed with the Old Testament writers.
He regarded the words of the Old Testament writings
as being the words of God.
He submitted to them in his own life,
he believed them,
he accepted their statements,
and sought to apply their principles.
He regarded Scripture as the great arbiter in dispute.
He said to his contemporaries,
"You make many mistakes,
because you don't know the Scriptures."
We find in the New Testament
that he invested the apostles with authority
to teach in his Name.
He said that the Holy Spirit
would lead them into all truth,
would bring to their remembrance what he had spoken
and would show them things to come.
He evidently expected
that in the providence of God
there would be others to interpret,
and bear witness
to the revelation given in himself,
just as there were prophets raised up by God
and inspired to bear witness
to what he did in Old Testament days.
To sum up,
the authority of Scripture
is due to the inspiration of Scripture.
The Old and New Testaments
are authoritative in our lives,
because they are in fact inspired.
since Jesus Christ is our Teacher
as well as our Lord,
the authority of Christ and the authority of Scripture
stand or fall together.