C3.2

determine, through investigation with technology (i.e., 3-D graphing software) and without technology, that the solution points $(x,y,z)$ in three-space of a single linear equation in three variables form a plane and that the solution points $(x,y,z)$ in three-space of a system of two linear equations in three variables form the line of intersection of two planes, if the planes are not coincident or parallel Sample problem: Use spatial reasoning to compare the shapes of the solutions in three-space with the shapes of the solutions in two-space for each of the linear equations $x=0$, $y=0$, and $y=x$. For each of the equations $z=5$, $y-z=3$, and $x+z=1$, describe the shape of the solution points $(x,y,z)$ in three-space. Verify the shapes of the solutions in three-space using technology.