For any given line L, if the intercepts are given, we can write the equation of the line as $\frac {x} {x-intercept} + \frac {y} {y-intercept} -1 = 0$

For the given line, it stands as L = $\frac {x} {6} + \frac {y} {3} -1 = 0$ Now, notice that when the value of origin is plugged in (0,0), we get L as 0+0-1 --> L<0. Thus, the origin lies on the negative side of the given line. And, as origin lies below the given line, all the points in that region will make L<0 -->

$\frac {x} {6} + \frac {y} {3} -1<0$ --> $\frac {y} {3}< 1-\frac {x} {6}$ --> $y < 3-\frac {x} {2}$

Answer: E