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Default Line chart for churn rates of many items over time

I have a set of data that tracks the number of changes to a file over
time. I want to show a line chart that I can use to visually locate a
file with a low churn rate. "Low churn rate" could either mean "Has
changed a lot in the past but hasn't changed in a while" or it could
mean "has the lowest number of changes happening to it right now."

The purpose of this is that we have a set of operations we want to
perform on files, but only if they are fairly stable and either aren't
getting changed often, or haven't changed in a while.

My data is something like this:

FileID,ChangedDate
1,8/23/2005
1,8/24/2005
1,8/25/2005
2,8/23/2005
3,8/23/2005
4,8/23/2005
4,8/24/2005

I'm having trouble wrapping my mind around how exactly I want this to
look graphically. I definitely want the X axis to be time and I want
one line in the chart per FileID, but I'm not sure about how to
configure the Y axis to reach my goal of allowing me to visually pick
out a "low churn" file.

If I were to just have "Count of changeddate per fileid" as the Y axis,
then all I get is a flat horizontal set of rows which just tells me a
file has churned a certain amount, it doesn't tell me if it's churning
less now than it was a month ago.

If I make it a bar chart with the X axis of FileID and the Y axis
ChangedDate, with the data portion being Sum of FileID, that *kind of*
gets me what I want, because you can visually pick out the FileIDs that
have a lot of bars next to them. The problem with this is that I expect
to have hundreds if not thousands of FileIDs at some point, so I need
something to help me visually pick those out... and perhaps a line
chart isn't it, but it seems closer than anything else.

Any pointers much appreciated, thanks.