Geometric representation of the plane $y+2z = 1$ I am trying to wrap my head around the geometric representation of the plane $$y + 2z = 1$$.
I know I can rewrite the equation on this form: 
$$0x + y + 2z - 1 = 0$$
So $x$ can assume any value, but what does this actually mean? How would that plane look? 
 A: If $x$ is not in the plane equation, then this plane is perpendicular to the coordinate $(y, O, z)$ plane.
Like in two-dimensional case - the equation $y=1$ ($x$ is not in this equation) defines a straight line, perpendicular to the $(O, y)$ axis.
And in general, any equation $F(y,z)=0$ defines cylindrical surface in three-dimensional space, which is perpendicular to the $(y, O, z)$ plane.
A: Terminology could be sometimes imprecise and confusing. What one really means by saying "$y + 2z = 1$ represent a plane" is that the set
$$
\{(x,y,z)\mid y+2z=1\}\tag{1}
$$
which is a subset of $\mathbb{R}^3$ can be visualized as a plane. The set in (1) can be read as

the set of all the points $(x,y,z)$ in $\mathbb{R}^3$ which satisfy the equation 
  $$
y+2z=1.
$$

If you want to know about why (1) is a plane in the Euclidean space, you could read this Wikipedia article. 
A: Another way to think about this is to draw the line y+ 2z= 1 in yz-plane.  When z= 0, y= 1 and when y= 0, z= 1/2 so this is the line through (1, 0) and (0, 1/2)- again that is in the yz-plane.  That line extends to the plane parallel to the x-axis.
