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So this is a 3D plane, isn't it?

yes

eek 3-d. vectors all over again

Remember that when x, y are 0 then z is 6, when x, z are 0 then y is 6 etc

So plot the points on the intercepts first.

it has to be a plane, so it shouldn't be hard to make out the shape from there.

how would this look

Also, it has a normal vector of <1, 1, 1> so it is perpendicular to that vector.