"Find all values of such that the slope of the line through the points and is less than 5."

I solved it by first finding the slope which simplifies to . Then I used the point-slope form to derive the equation . Then, I got lazy, and plugged in a couple of test numbers into the equation, found that numbers above 2 seemed to qualify, and decided that the answer was the set . Unfortunately, the answer should have included also the set .

Algebraically, what should I have done to get to that answer? What part did I skip?