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Let $l$ be a line with slope $\frac{1}{0}$, and $m$ a line with slope $0$. Now, line $l$ is perpendicular to line $l$, therefore the product of the slope of line $l$ and the slope of line $m$ equals $-1$. This implies that $\frac{1}{0} \times 0 = -1$!

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  • $\begingroup$ the slope of the vertical line is not defined as division by zero is not defined $\endgroup$
    – Vikram
    Dec 19, 2016 at 6:58
  • $\begingroup$ We can "prove" all sorts of things using division by zero... There is even a section on division by zero "proofs" at the Wikipedia Mathematical Fallacy page, which contains the famous "proof" that 1=2. $\endgroup$ Dec 19, 2016 at 7:18
  • $\begingroup$ Why are you posting twice? 1/0 is not a number so you can't manipulate it arithmetically like that. If 1/0 x 0 equals anything, then it has to equal everything. But it doesn't equal anything. $\endgroup$
    – fleablood
    Dec 19, 2016 at 7:28
  • $\begingroup$ Sorry my mistake. But that is not the answer to my question $\endgroup$ Dec 19, 2016 at 7:32
  • $\begingroup$ Kanwaljit singh gave the answer with reasons..!! $\endgroup$ Dec 19, 2016 at 7:34

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As per wikipedia

"Two lines are parallel if and only if their slopes are equal and they are not the same line (coincident) or if they both are vertical and therefore both have undefined slopes. Two lines are perpendicular if the product of their slopes is −1 or one has a slope of 0 (a horizontal line) and the other has an undefined slope (a vertical line)."

So, it is obvious that the rule of multiplication of slopes is not applied when one of the line is vertical and another horizontal. Further, y-axis (or more specifically, the line x = 0) doesn't have a slope of infinity but it is undefined.

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