Triangle abc is similar to triangle def. using the image below, prove that lines bc and ef have the same slope. you must show all of your work to receive credit. triangle abc and def are shown. a is at negative 2, 1. b is at negative 2, 4. c is at 1, 1. d is at 4, 2. e is at 4, 4. f is at 6, 2.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.