Keyframes are set to Linear but they are not Linear

Hello, I am animating some still images and am running into a problem that is making me think I'm crazy. I have animated the images by adding keyframes to the position. Most of the keyframes are working correctly, but even though all keyframes are set to Linear, some of them are not working linearly. For example, one keyframe is set to 567.8 position, then the next keyframe is set to 540. I would expect that since all keyframes are set to Linear then the figures in between the keyframes should go down from 567.8 to 540 incrementally. However, what its actually doing is hitting 540 prematurely (around 3/4 of the way in between the keyframes), then its dropping down to 533.1 (around halfway between 3/4 of the way to the next keyframe and the next keyframe itself, or 7/8 of the way between the two keyframes), then it reverses course and goes back to the 540 that the final keyframe is set to. I am under the impression that this is not how it should work with Linear keyframes, and that they should just go from one to the next in a straight line. So why is it hitting the next keyframe early, going past the point that the next keyframe is set to, and then bouncing back to the match the keyframe? Any help would be grately appreciated.