the graph of 2x+y=2 is a line L through the points (0,2) and (1,0). Describe the graph of 2x+y is greater than or equal to 2.

Question

I've been stuck on this question and I do not know how to answer it.

 

The options are:

 

A) Half-plane containing the L as its boundary and containing the origin.

B) Half-plane containing the line L as its boundary and not containing the origin.

C) Half-plane not containing the line L as its boundary and containing the origin.

D) Half-plane not containing the line L as its boundary and not containing the origin.

Answer 1

Okay, if you graph line L, you can clearly see it just missed the origin (0, 0).  Graph this line first.  

 

An inequality of greater than or equal means that the line is solid, not dashed.  Therefore, solutions along the line are included so we can eliminate answer choices C and D since they state that the "not containing the line" and clearly this is wrong because a solid line means that solutions are contained.

 

Graphing a greater than or equal inequality means to shade above (right) of the line y=-2x+2.  Shade this region.  You can see that the origin is not contained in the shaded region, therefore, it is not part of the solution.  This lets us eliminate A, which states that it contains the origin.  That leaves us with answer choice B.