Question about epipolar lines and essential matrix

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I am reading up on essential matrices and I got a little bit confused. Why does Ex (or x'E) give us the epipolar line ? Where E is the cross product of t and R ? Doesnt it just give the direction of x' ?

Can I look at it another way ? i.e. because t and R, the translation-rotation matrix aligns both frames to be parallel, the epipolar lines in the aligned frame is a straight horizontal line. And in the "original" frame it looks that way like in the image.