When you subtract y-coordinates of two points, you're just finding the distance between them purely in the vertical direction. That's sometimes called the "rise". Similarly when you subtract x-coordinates of two points, you're finding the purely horizontal distance between them, sometimes called the "run". So Statement 2 just tells us "rise = run", or dividing on both sides, "rise/run = 1", so it tells us the slope of the line is 1. That's not sufficient to answer the question, because we have no idea where the line is, but using Statement 1 along with Statement 2, we know exactly what line we're dealing with, so of course we can answer any question about it.
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