Both are correct. You can also use this format: You can put someone's life into jeopardy by ....

The singular should be 'life', not 'live'. If you change the second sentence to say "someone's life", then either is good. Personally I prefer the first one though. -- Life vs. live -- Many people's lives, one person's life. (laɪv / laɪf) He still lives here, he used to live there. (lɪv / lɪf)