Question

There are some interesting special cases in which the graphs turn out to be parallel, perpendicular, or coincident with the coordinate planes or axes. Sketch a graph of each of the following equations by drawing their traces as in Problem 1. Then tell what the graph is parallel to, or coincident with.

b. y+z=4
I got y=4 and z=4 and what do i do next? I don't really understand what the question is asking.

c. x+y=0

e. x=5

Answer 1

Any line in the yz plane becomes a plane perpendicular to the yz plane, in xyz space.

Think of the point y=3. When propagated parallel to the x-axis (perpendicular to the y-axis), it becomes a line. Same for a line propagated through space.

x+y=0 is the same thing, parallel to the z-axis.

x=5 is a line (xy) or a plane (xyz) perpendicular to the x-axis.