When I zoom in on a plot containing a variable line, the line shifts away from the data. Why?

The problem is that you are zooming in so much that the points used to draw the line are so far away from the area being zoomed into that the line shifts away from where it should be. One workaround is to include some points within (or just outside) the limits that you wish to view. This way the data points aren’t spread so far apart and you can zoom in further on the data.