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The equation $z=a x + b y$ defines a plane passing through the origin of coordinates $(x,y,z)$. If the plane is horizontal, i.e., perpendicular to the $z$ axis, the range of $z$ values is just $[0,0]$. That corresponds to $a=b=0$. For all other $a,b$ the plane is tilted with respect to the horizontal plane, and the range of $z$ values for points on the plane ...


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