Equity P/E

First what’s the difference b/t implied, intrinsic, and justified P/E? Second I saw this question and am a little confused. ^ might be a clue. Implied P/E ratio is 53. Index growth rates move from 4% to 5%. Is the new P/E higher or lower. I said higher because: P/E = (1-b)(1+g) /k-g. Answer said the implied P/E and the index growth grate are negatively related. I suppose this is a different growth rate. Anyhow I’m confused.

implied - based on market P, justified = intrinsic - based on fundamentals