Ok here goes ( assume ? denotes greter then equal to)
(We will consider the same problem y>3x?9 (I made 7 into 9 for simplicity)
Break the problem into two parts:
1)y>3x
2)3x?9 which becomes x?3
a) Now first plot y=3x
This will pass through the origin with slope =3.
(Slope = -a/b if the equation is ax+by=c and this is 3x-y=0 so a=3 and b= -1)
b) Now since we need to plot y>3x and not y=3x ..this will be the entire region on one side of the line. To find out which side.
Take ANY point which does not lie on this line ( like x=5, y=5)
Since this does not satisfy y>3x as 5 is not>15....The required region will be the entire region on one side of y=3x not containing (5,5).
c) Now we are left with x?3. So again by the same procedure you get the region on the right side of the line x?3 (but also include the line itself as we have ? and not >).
d) Now take the intersection of the two regions. PROBLEM SOLVED