On the line is an American English Idiom which generally means:
- If something is on the line, it is at risk of failing, or being harmed or something is in a situation in which it could be lost or harmed. Most times it is used in reference to work. So it means in danger of losing one's job and/or reputation.
- Or on the line could simply mean speaking on the telephone: John was on the line talking to his mom.
So to re-state the above pictured example:
Stacey was trying her best to improve her work skills sincer her company was cutting back on expenses and feared she may be in danger of losing her job, if she doesn't do something soon to impress them!
John's verbal abuse at the news reporter was shocking. Now his good reputation will be on the line.
John's verbal abuse at the news reporter was shocking. Now his good reputation will be at risk of being harmed.
Tracey's life is on the line, if she doesn't receive a kidney from a donor soon.
Tracey's life is at risk of failing, if she doesn't receive a kidney from a donor soon.