"Find all values of $\displaystyle r$ such that the slope of the line through the points $\displaystyle (r, 4)$ and $\displaystyle (1, 3 - 2r)$ is less than 5."

I solved it by first finding the slope $\displaystyle \frac {2r + 1}{r - 1} = 5$ which simplifies to $\displaystyle r = 2$. Then I used the point-slope form to derive the equation $\displaystyle y = 5x + 16$. 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 $\displaystyle (2, \infty)$. Unfortunately, the answer should have included also the set $\displaystyle (-\infty, 1)$.

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