Hello, I am a little confused on how to prove these half planes are convex, and my book does not actually show an example. ---------- So here is a problem, my book briefly talks about it: Show that the plane 2x - 3y >= 6 is convex. So if we let A = (2,-3), and X = (x,y), then we can write the inequality [itex]A \cdot X >= 6[/itex]. Prove that this half plane is convex. --------- So I want to let there be a point P in this half plane, and a point Q on this plane, and then show that (1-t)P + tQ is of the same form and therefore the half plane is convex. The problem I am having is what do I let P and Q be equal to, in order to show this? Thanks.