How to find the coordinates of intersection points between a plane and the coordinate axes? Can you please explain what I am supposed to do and why that is true?
The equation of the plane is $4x - 3y = 12$.
Is the $z$ coordinate always zero in this plane or not? I mean, it is, if its the 
XY-plane, but this doesn't seem to be the case?
Where does this plane cut the $x$-axis, $y$-axis and $z$-axis?
Thanks a lot.

Basically $z$, in the equation $4x-3y=12$ has the potential to be any point. Since we are given an equation with $x$ and $y$ only, and we are graphing this in $3$d space it is going to extend out to an infinite amount of $z$.
