x+2y+3z=6
Plane xy
z=0→x+2y+3(0)=6→x+2y+0=6→x+2y=6
x=0→0+2y=6→2y=6→2y/2=6/2→y=3→Point=(x,y,z)=(0,3,0)
It's not the first graph, because at plane xy when x=0, y=2
In the second and third graph, at plane xy, when x=0, y=3
y=0→x+2(0)=6→x+0=6→x=6→Point=(x,y,z)=(6,0,0)
It's not the third graph, because at plane xy when y=0, x=3
It's the secon graph, because at plane xy when y=0, x=6.
Let's check the other planes:
Plane yz
x=0→0+2y+3z=6→2y+3z=6
z=0→2y+3(0)=6→2y+0=6→2y=6→2y/2=6/2→y=3→Point=(x,y,z)=(0,3,0)
In the second graph, at plane yz, when z=0, y=3
y=0→2(0)+3z=6→0+3z=6→3z=6→3z/3=6/3→z=2→Point=(x,y,z)=(0,0,2)
In the second graph, at plane yz, when y=0, z=2
Plane xz
y=0→x+2(0)+3z=6→x+0+3z=6→x+3z=6
z=0→x+3(0)=6→x+0=6→x=6→Point=(x,y,z)=(6,0,0)
In the second graph, at plane xz, when z=0, y=6
x=0→0+3z=6→3z=6→3z/3=6/3→z=2→Point=(x,y,z)=(0,0,2)
In the second graph, at plane xz, when x=0, z=2
Answer: The second graph