In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?b/a⋅c/d=−1b/a=c/db/a=d/cb/a⋅d/c=−1

b/a=c/d Two lines are parallel to each other if they have the same slope. So let's look at the options and see which one matches that statement. b/aâ‹…c/d=â’1 * This is checking to see if the two lines are perpendicular to each other. Almost the exact opposite of parallel. So this is the wrong answer. b/a=c/d * b/a is a legitimate slope. c/d is also a good slope. And they're being checked to see if they're equal to each other. So this is the correct answer. But let's see if the next two options will give us a chuckle or two. b/a=d/c * b/a is OK. d/c almost looks ok, check the figure. And d/c is NOT a slope. The slope is delta Y over delta X. And d/c is delta X over delta Y. The inverse of the slope. So comparing those two values is meaningless. So it's a wrong answer. b/aâ‹…d/c=â’1 * And they're trying the inverse of the slope trick again. WRONG. And they're checking if it's perpendicular. Also wrong. So definitely not a good choice.