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I want to ask what is the use of Families of straight lines?

I am thinking of A Family of Straight Lines Passing Through the Intersection of Two Lines.

We have the equation: L1+kL2=0 where L1=L2=0 and k is a variable, right?

But is it said that L2 is not included in this family?

So why are we using this equation, when it cannot fully represent all the lines with this common properties, so as to classify them into a family?

Please, may you help. Thanks

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# Families of straight lines

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