How to grab two points from linear equations and from a matrix m.x == b for the purpose of creating lines or planes from each row.?

Question

Don't get me wrong I can easily do it on paper and I could probably write convoluted code that will get the job done but I feel like there has to be an easy Mathematica way to do this. A few users on here came to my rescue and showed me how to plot linear equations from a matrix but they use ContourPlot and ContourPlot3D. I want to try to do this with other graphing options such as Plot and Plot3D. Below I have a few samples of matrices I wish to create lines and planes from. I think the key here is to find an efficient way to grab two or three points from each matrix row or equation.

    (* line's and plane's from this *)
    m3 = {{1, 0, 1}, {-1, 3, 1}, {3, 4, 5}};
    b3 = {3, 2, 4};

    (* line's from this *)
    m2 = {{1, 2}, {3, 1}};
    b2 = {1, -2};

   (* These are the resulting linear equations and solutions *)

    Det[m2]
    eqns = m2.{x, y} == b2
    Solve[eqns, {x, y}]
    Reduce[eqns, {x, y}]

    Det[m3]
    eqns = m3.{x, y, z} == b3
    Solve[eqns, {x, y, z}]
    Reduce[eqns, {x, y, z}]

Answer 1

Maybe this way with Hyperplane? Note that the $i$-th row of the matrix is a normal vector to the hyperplane defined by the $i$-th equation.

m3 = {{1, 0, 1}, {-1, 3, 1}, {3, 4, 5}};
b3 = {3, 2, 4};
p = LinearSolve[m3,b3];

Graphics3D[{
  Sphere[p, Scaled[0.02]],
  Table[Hyperplane[n, p], {n, m3}]
  },
 PlotRange -> All
 ]