Let $x$, $y$, $z$ be three collinear points in homogeneous coordinates. Show there are scalars $j$, $k$, and $l$ such that $jx + ky = lz$, with $j$, $k$, and $l$ not all $0$.
I started with the definition of collinear points. That is, $jx_i + ky_i + lz_i = 0$, with $j$, $k$, and $l$ not all $0$.
Then I continued by saying that $jx_i + ky_i = -lz_i$.
I'm stuck and would appreciate some help. Thanks. I hate geometry.