It is coordinated geometry
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A network of lines used for locating points is a coordinate grid
the coordinate plane is a map of points
Points with integer coordinates are often called lattice points. Lattices exist in all dimensions.When we talk about lattices points on the rectangular Cartesian coordinate system, this is a two dimensional lattice. Three dimensional lattice points are often used to study crystals.
It is called a graph. Graphs consist of many such points.
All points whose y-coordinate is twice its x-coordinate.