I tried to do this sum by visualizing myself drawing 8 parallel lines of a paper. I can't visualize how many non overlapping region will form. And I don't know whether I should consider the edges of the paper as parallel lines or not.
Please Explain like you're teaching a kid. (Started Maths From Scratch!) Help is much appreciated!
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The base case is an empty sheet: before you draw any line, you have $1$ region.
Then, every new line, not crossing or overlapping another lines, divides a region in which it is drawn into two, hence increasing the total number of regions by $1$. Eventually, after drawing $n$ lines you have $1+n$ regions.
If you draw $1$ line then you create $2$ regions.
Every new parallel line will split up an existing region in $2$ regions, so will make the total number of regions increase with $1$.