Product of slopes of pirpendicular lines is -1. Slope of x-axis is 0, slope of y-axis is “infinity”. But, 0*infinity is not -1 why?

we say product of slopes  -1 if perpendicular when both slopes are finite

if one of them is infinite then use the formula again 

tan (teta)=(m₂-m₁)/1+m₁m2

              =(1-(m₁/m₂ ) )/(m₁+1/m₂ )

now put m₂ infinit  and m₁ =o

u get tan (teta )as 1/0 so teta=90⁰    

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If product of slopes of 2 lines is -1 then they are perpendicular. But, the converse may not be true always. The statement of converse clearly has a limitation in it i.e., if the lines are parllel to the coordinate axes this statement dosent hold good.