JESUS - Acts 16:31

They (Paul and Silas) replied, "Believe in the Lord Jesus, and you will be saved--you and your household."

Believe 
John 3:14-18  "Just as Moses lifted up the snake in the wilderness (Numbers 21:8-9), so the Son of Man must be lifted up, that everyone who believes may have eternal life in him." For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God's one and only Son.

and you will be saved 
Romans 11:13-14  I am talking to you Gentiles. Inasmuch as I am the apostle to the Gentiles, I take pride in my ministry in the hope that I may somehow arouse my own people to envy and save some of them.

you and your household 
Acts 11:13-14  "He (Cornelius) told us how he had seen an angel appear in his house and say, 'Send to Joppa for Simon who is called Peter. He will bring you a message through which you and all your household will be saved.' "
Acts 10:43  "All the prophets testify about him (Jesus) that everyone who believes in him receives forgiveness of sins through his name."

(parentheses are mine)

Scriptures taken from the Holy Bible, New International Version® NIV®, Copyright© 1973, 1978, 1984, 2011 by Biblica, Inc.® Used by permission. All rights reserved worldwide. 
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