GridLines draws rectangular grid lines in the plane, but what I'm trying to do is to visualize grid lines by specific basis vectors. For example, the basis vectors are given as (1,1) and (-1,1), and I want to draw grid lines generated by multiples of those basis vectors. How do I do this?

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    $\begingroup$ something like Graphics[InfiniteLine[{0, 0}, #] & /@ {{1, 1}, {-1, 1}}]? $\endgroup$ – kglr Jan 28 at 1:22

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