Question

Which graph correctly represents 1/3y-1/2x>2 ?

Answer 1

Put it in the form of y =mx +b, or in this instance, y> mx +b 
move the (1/2) x to the right by adding it to both sides of the inequality 
(1/3)y>(1/2)x +2 
Multiply by 3 on both sides to get y by itself. 
y>(3/2) x +6 
This is a graph with y intercept of (0,6) and a moderate upward and to the right slope. Because it is > , the line on the graph will NOT be part of the solution. 

The easiest way to find the side of the graph that the inequality satisfies is to use (0,0) and see if it works or doesn't work. In the original equation, 0-0>2 does NOT work, so the area where the inequality works is to the up and left of the graph, which should be a dotted line to show that the inequality is greater than only. 
The point (6,-2) should work.
Test it. 6*(1/3)-(-2)*(1/2)>0 ; 2-(-1)=3, and 3>2 It does work. 
The point (6,2) should not work 
Test it. 6 *(1/3)-2(1/2)=2-1 ; 1 is NOT >2, so it does not work. 
If the graph goes through the origin, then pick a point near the graph with a small x or y.