Find the points at which the plane 3x-4y+z=12 intersects the coordinate axis and find the equations of the lines where the plane intersects the coordinate planes.
To find the x-intercept set the y and z coordinates equal to zero. This gives
Now do the same thing with y and z, set the other two coordinates to zero.
To find the equation of the line in the xy plane, set
This gives
Again do the same thing with the other two coordinates.