Evelyn,
Lay the two pieces end-to-end, with about four inches overlapping. The raw edges of the two pieces should make a continuous line. Cut the two pieces at an angle (not necessarily at 45 degrees) at once using a longer ruler. Then lay the "new" raw edges together right sides together in preparation to stitch. When you do this, there should be rabbit ears sticking up at the 1/4" seam line. These "ears" can be trimmed after stitching. Again, once stitched, you should have a continuous straight line.
You can use this method with attaching pieces of binding together. Infact, I stack several atop each other and cut several at once being careful to cut the opposite end at the same angle.
Suzanne