x > 2y
First draw the graph of the boundary line x = 2y. Draw it dotted because the
line is the boundary of the graph and is NOT included in the graph:
Now follow these rules:
1. If the inequality is solved for x, and it is "x<" or "x<, then shade the region which is to the LEFT of the line.
2. If the inequality is solved for x, and it is "x>" or "x>, then shade the region which is to the RIGHT of the line.
3. If the inequality is solved for y, and it is "y<" or "y<, then shade the region which is BELOW the line.
4. If the inequality is solved for y, and it is "y>" or "y>, then shade the region which is ABOVE the line.
Yours is case 2, so we shade the region to the right of the line:
Notice that if we solve it for y:
x > 2y
> y
that is the same as
y <
which is case 3, and we would shade BELOW the line, but that is the
same region, because the region BELOW the line is also the region
which is to theRIGHT of the line. So there will never be a conflict
in the rules. You may solve for either letter. The region to shade
will always be the same region, regardless of which variable you
solve it for.
Edwin
