Answer
Please see the figure attached.
Notes:
- Red dashed lines are the vertical traces parallel to the $xz$-plane
- Black dashed lines are the horizontal traces
Work Step by Step
We have $f\left( {x,y} \right) = 12 - 3x - 4y$. By setting $y=a$ we fix the $y$-coordinate and obtain the vertical trace $f\left( {x,a} \right) = z = 12 - 3x - 4a$ that lies in the plane parallel to the $xz$-plane. Similarly, we can set $x=a$ to fix the $x$-coordinate and obtain the vertical trace $f\left( {a,y} \right) = z = 12 - 3a - 4y$ that lies in the plane parallel to the $yz$-plane.
The horizontal traces are the lines $c = 12 - 3x - 4y$. So,
$4y = 12 - 3x - c$
$y = \frac{1}{4}\left( {12 - 3x - c} \right)$
