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because, when you go, lets say, (2,3), and the line is on the 2, you change the second number, not the 2, but the 3.
The slope of a line is the ratio of rise over run. On a vertical line you have an infinite rise over zero run. Your slope would be infinity/0. As you know, you cannot divide by 0, so the slop is undefined.

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Q: Why do vertical lines have an undefined slope?
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