Then we pick a point on one side of the line to see whether that point should be included or not. A nice point we can use is (0, 0). If we decide it can't be included, we'll hang a "No (0, 0) Allowed" sign on the clubhouse door and tell everyone else in the treehouse not to acknowledge him.
When x and y are both zero, the left-hand side of the inequality is
2(0) + 4(0)
which is indeed less than or equal to 1. That means we do want the side of the line with (0, 0), so we shade in that side of the graph:
When an inequality is strict, we do the same thing as above except that now we don't want to include the points on the line. In fact, we don't want to do anything that might upset it, considering how strict it is. We are so over being grounded.
To show that we aren't including the points on the line, we draw a dashed line instead of a solid line.