SOLUTION: 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. The options are: A) Half-plane containing the l

Algebra ->  Graphs -> SOLUTION: 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. The options are: A) Half-plane containing the l      Log On


   



Question 1115719: 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.
The options are:

A) Half-plane containing the line 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.
Also if you can explain why the answer that would help a lot!

Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
In case you are unsure, solve for y in terms of x.
2x%2By%3E=2
y%3E=-2x%2B2
The solution includes the line and all values above the line (all points above the line).

Choice B.

You could recheck if you want, but you can easily visualize or draw the graph and see if Origin is or is not in this half-plane.

0%3E=-2%2A0%2B2
0%3E=2------FALSE - so point (0,0) is not part of the solution.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2By=2, ->y=-2x%2B2
2x%2By%3E=2->y%3E=-2x%2B2


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+y=-2x%2B2%2C+y%3E=-2x%2B2%29+

as you can see, answer is:
B) Half-plane containing the line L as its boundary and not containing the origin.