Hi dyan208.
If the fault were with the display itself, the line being persistent would be expected. Intermittent lines often point to an issue with the cable that connects the display to the logic board.
While it's impossible to say for sure without being able to physically inspect the device, there is a series of steps you can take to fully isolate the issue.
If you're already running the most up-to-date version of iOS (iOS 13.5.1 as of the time of this post), you may need to consider reinstalling iOS on your device. While this shouldn’t affect any data stored on the iPhone, it would be a good idea to make sure you’ve got a backup in place:
How to back up your iPhone, iPad, and iPod touch - Apple Support
Once you’ve successfully backed up your device, follow these steps to reinstall iOS, making sure to choose “Update” when prompted:
If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support
If the issue persists, do the restore process again but this time, initially set the device up as new, without restoring the backup. Use it that way for a bit to see if the issue with the display is resolved. Once you know if it's resolved or not, do the process again and this time apply the backup. If the issue is resolved when the device is set up as new but returns when the backup is restored, then you'll know the issue is something in the user data. If it's still there when the device is set up as new, then the issue is hardware.
Cheers.