Sketch a graph in the xyz-space and identify the plane as parallel to the xy-plane, xz-pane, or yz-plane and sketch a graph.
a) y = 4
b) x = -2
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I don't understand why the answer for (a) is plane parallel to xz-plane!
Well, do you know what "xyz- space" means? Do you understand that any point (x, y, z) satisfying y= 4 is of the form (x, 4, z) where x and y can be any number. The distance from that point to the xz-plane is the distance from (x, 4, z) to (x, 0, z), 4. The set of points that are all a fixed distance from the xz-plane is parallel to the xz-plane.
The xz-plane is all points in xyz space where y=0, x is anything, and z is anything.
All points where y=4 means that x can be anything, z can be anything, and y must be 4.
I am not sure I understand what you are not understanding? Is it a question of notation? Are you confused about definitions? Visualizing subsets of 3-space is complicated, so there are many areas that might be causing you confusion. I don't want to waste time explaining something that you already know and understand well.