Esther Hi'ilani Candari
Lines are most likely the first art element you learn to create, whether it was with a crayon, pencil, or paintbrush.
One thing to remember when talking about lines in context of art is that the definition is broader (literally) than a mathematical line. In mathematics a line is purely one dimensional, it only has length. But in art, as well as mathematical visualizations, a line has width and that width can vary widely. This variation in width is called weight. 

Another way the definition of a line is broader in art is

 the inclusion of actual and implied lines. Implied lines are elements in an art piece that function as a line even if they are not created by a continuous mark. The easiest example is a dotted or a dashed line. The individual dots are just little shapes but because they are lined up they become a line because that is how our brain sees them. 
An even more conceptual line that you will see used in many art pieces is the "line of sight".

This is the term for the invisible connection created between a set of eyes in an image and the object or person they are observing. The reason this is classified as a line is because you as the viewer follow that line of sight as if it was a visible path across the image. Our minds automatically want to look at what other people or creatures are looking at. This line can be a powerful way to draw your viewers attention to important elements in your image.
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Another term that is often used to describe lines in art is "dynamic". This typically refers to lines that change direction and weight in energetic and engaging ways. 

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