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
$\displaystyle 3x-4(0)+0=12 \iff x=4 \iff (4,0,0)$
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 $\displaystyle z=0$
This gives
$\displaystyle 3x-y=12 \iff y=3x-12$
Again do the same thing with the other two coordinates.