Equality of pairs of parallel lines.

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In the picture above two sets of parallel lines are given: $l, m$ and $p, q$. when can we say these pairs are the same? If the distance or altitude are same then can we say they are equal?

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2 Answers

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I think that they will be equal if they represent same set of equations. For instance if the set of two lines l and m have equations $2x+3y=8$ and $2x+3y=6$ while the p and q have equations $2x+3y=8$ and $2x+3y=6$ (in any order) then these two sets of lines will be equal.

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It depends on your definition of equivalence class. You can define two lines equivalent if they are parallel. I don't know if this is what you meant.

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