Slope: Why A Vertical Line Has An Undefined Slope In Mathematics

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A vertical line does not have a slope because its slope is undefined. This is because a vertical line is perfectly upright and has no horizontal change. Since slope is defined as the change in y over the change in x (rise over run), and a vertical line has no run – its run is zero – we cannot divide by zero to find its slope. Therefore, we say that a vertical line has an undefined slope.

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