For many years the people of Israel prayed for a savior who would draw them back towards God, and restore their nation. They studied prophecy about this coming savior so that they would be able to know when he comes, and celebrate his arrival. And yet, Jesus comes into the world without notice, leads three years of ministry, mostly without notice from the very people studying so they would not miss him.
In Ezekiel God makes a covenant with Israel, that sounds a lot like wedding vows (because it was meant to be a wedding vow). God promises to transform their (and our) hearts as we follow after him passionately. That part of following God is that it changes us deeply.
In Acts 9 we meet a woman named Dorcas who seems to be living a relatively normal life. Then she passes, and the town begins to turn out in large numbers to remember the simple, everyday ways that this woman served and blessed her community. From a place of gratitude to God, we each are invited to serve and love others out of the overflow of our relationship with God.
In the Sermon on the Mount Jesus outlines a variety of ways that we are to live out our faith. Part of that is an assumption that to believe in Jesus changes our lives, and how we live. The word for belief in the bible assumes that you both comprehend and agree with something in your mind, and that your knowledge of that transforms your heart, mind, and actions.