Select the verts, then S-Z-0 (zero). This Scales the vertices so they move along the Z-axis only; scaling to zero makes them line up. You will then have to move them all as a group to match with the red line. There are more precise ways to do this snapping that escape me right now.*
Edit: *Oh yeh, place the 3D cursor on the red line. Period key to make the 3D cursor into the pivot point. Then S-Zed-Zero. The verts will line up with the cursor. Both of these methods only work if your target line is parallel to one of the cardinal axes, which in your example is true.