Running throughout the month of October, Becky’s Lines&Squares challenge will make you realise that every photo you’ve ever taken has at least one line in it.
My submissions feature multiple sets of lines that are confusing if we allow the eye to trace them all, comparing and contrasting, particularly the picture of reflections in a city shop window. In each picture, we have to step back from exploring the lines to see the whole: an interesting exercise.
Susan Rushton 
You did a nice job with abstractions in these images.
The nature photographer in me begs to differ with your statement that “every photo you’ve ever taken has at least one line in it”—assuming that by “line” you mean “straight line”. Your statement is often true for photographs that include human elements like those in this post’s four pictures. On the other hand, many nature photographs show no straight lines.
I was interpreting lines very loosely, including curved and wavy lines – I suppose anything with progression or outline. You are very much in tune with Oddment’s comment about her drawing instructor’s words (in the comments above).
“Line” used to mean what we would now call “curve”. People sometimes still use the word in the older sense, as you say you do. It was the ambiguity that led to the creation of the unambiguous term “straight line”, which mathematicians see as a redundancy because in the technical sense a line is necessarily straight.
It’s interesting how words change their meaning. I’d see a need for a modifying word – straight, curved, wavy, meandering – to define a particular type of line, but I am not a mathematician.