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I want to perform a simple calculation to move an image along the video with given frames as the length of the animation:

overlay=x='( 1 * INDEX)':y='(1 * INDEX)':enable='between(t,438/25,450/25)'

Obviously INDEX doesn't exist, but for the start frame of 438, I want index to equal 0, for the frame 439 I want INDEX to equal 1, and so on and so forth.

The goal is to have the image move one pixel for every frame after 438 and hide it at frame 450

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Just subtract the first frame index from the expression:

overlay=x='n-438':y='n-438':enable='between(t,438/25,450/25)'

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