The brief
Take a number of shots using lines to create a sense of depth. Shooting with a wide- angle lens (zooming out) strengthens a diagonal line by giving it more length within the frame. The effect is dramatically accentuated if you choose a viewpoint close to the line.
Now take a number of shots using lines to flatten the pictorial space. To avoid the effects of perspective, the sensor/film plane should be parallel to the subject and you may like to try a high viewpoint (i.e. looking down). Modern architecture offers strong lines and dynamic diagonals, and zooming in can help to create simpler, more abstract compositions.
Review your shots from both parts of Exercise 1.3. How do the different lines relate to the frame? There’s an important difference from the point exercises: a line can leave the frame. For perpendicular lines this doesn’t seem to disrupt the composition too much, but for perspective lines the eye travels quickly along the diagonal and straight out of the picture. It feels uncomfortable because the eye seems to have no way back into the picture except the point that it started from. So another ‘rule’ of photography is that ‘leading lines’ should lead somewhere within the frame.
Investigation
The rule, as stated in this exercise, ‘leading lines should lead to somewhere in the frame’ is clear from the first 2 shots here. The first shot has the lines ending more or less on the intersection of top left third, on the horizon. The second is feels clipped with the leading lines leaving the frame on the left.
Why should this rule be the way it is? My theory on this …
The leading lines below accentuate the 3 dimensionality of the scene and take the observer on a journey into the frame. For us, our journeys need to have a destination so without some end point for the line the observer can’t see the journeys end, has no closure and is left frustrated. We live our lives with horizons and all lines tend towards those horizons, we typically either see the horizon or it is blocked from our view by some structure ( building, hill, trees etc ). Our lines then typically end at the horizon or at the blocking structure. To have the line end by exiting the frame therefore feels unnatural and constrained.
Wide angle 18mm focal length extending the leading lines, ending on the horizon. A strong image which leads the observer on the journey to the end of the road.

Leading lines leave the frame directly and the observer is left to wonder what this image is trying to portray. Is the fence itself the point?

The next two shots provide another example of the same concept of journey into the frame following the lines ( this time curved ). Observers eye is drawn into the frame, resting where the line disappears into the woods. There is a strong sense again of 3 dimensions in the frame and of a journey to be taken by the observer.

Here in contrast with the path clipped, most of the sense of 3 dimensions and journey is lost and the observer must search for the subject, which now becomes the plant pot in the top centre third.

To contrast this the next shots have strong lines but are intentionally flat with no sense of 3 dimensions at all in the frame. I used the high view point looking directly down (as referred to in the brief from László Moholy-Nagy ) to a carpet here .The lines serve no purpose other than to exist as an image for their own sake. There is no journey so no frustration with the lines not ending in the frame. This for me delivers a strong sense of purpose but without a narrative, the purpose is pure and aesthetic. To experiment with this theme the next 3 shots show lines in the frame in different directions, each has the same effect and impact.


Testing the theory of journey and horizon, the next two shots repeat the theme of leading lines which end in the frame and exit the frame. However this time there is no horizon per se as the lines lead straight into the sky. Again though the sense of completeness and closure where the lines end within the frame, present a far stronger intent to the observer. In the second image where the lines exit the frame, the observer is more likely to consider the centre of the frame and the tendency is to see these lines as pure and aesthetic and not a narrative or a journey to be had.


Although the image has infinite 3rd dimension into the frame, the angle flattens all lines and the image is pure and aesthetic. In this case the image here is reminiscent of https://www.theartstory.org/artist-moholy-nagy-laszlo-artworks.htm#pnt_6 László Moholy-Nagy first abstract painting in shape at least.

Summarising above
Leading lines take the observer into the frame and deliver a strong sense of 3 dimensions, of journey and narrative. This can help create a clear intent and purpose for the image. If however the lines have this intent but exit the frame, the narrative and purpose can quickly be lost and the observer is left to work out the purpose for themselves. Conversely where the image has a strong linear content where there is no 3rd dimension or journey accentuated, then those lines can become strong and pure with an aesthetic value in their own right, outside of any narrative.
References
https://www.theartstory.org – László Moholy-Nagy