"Therefore, since we have a great high priest who has ascended into heaven, Jesus the Son of God, let us hold firmly to the faith we profess." Hebrews 4.14
The implication of the verse above is that our faltering, inadequate prayers are perfected by Jesus and presented to God in such a way as to achieve their fullest effect. Moving out of petitionary prayer, for our own needs, into intercessory prayer, for the needs of others, extends our reach exponentially. Here's how...
When we love somebody or desire a certain course of events, we may do our best but can only achieve so much. When we bring this person or that situation to God in intercessory prayer, we are presenting the situation to him for whom all things are possible. We might still be involved as the answer to our prayer - or part of the answer. This might involve our needing to persist in that vein of prayer, not because our prayers are inadequate or ignored but because God, in his wisdom, discerns that the time is yet to be, or to fuel the desire which our prayer expresses. (Jesus told several parables to encourage persistence in praying.)
Jesus also extends the scope of our praying by instructing us to pray together and for our loved ones - and then to go the extra mile and pray for our enemies too. In this regard intercessory pray further transforms us by changing anger and resentment into compassion and grace.