SOLUTION: Sketch a graph of the solution of the system of linear inequalities. y≥1/2x+1/2 y≤4x−1/2

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Question 855779: Sketch a graph of the solution of the system of linear inequalities.
y≥1/2x+1/2
y≤4x−1/2
Answer by brysca(112) About Me  (Show Source):
You can put this solution on YOUR website!
When graphed, both linear inequalities should look like this:
+graph%28+300%2C+200%2C+-4%2C+10%2C+-4%2C+10%2C+%28.5%2Ax%29%2B.5%2C+4x-.5%29+
To graph both inequalities manually, follow the expression y=mx+b where m is the slope (rise/run), and b is the y intercept.
To determine the solution set between the two graphs, we must put a test point.
We will use point (0,0) for this example
Red graph:
y ≥ .5x+.5
0 ≥ .5(0)+.5
0 ≥ .5
Is zero greater than .5? Of course not, so shade the upper side of the red graph
Green graph:
y ≤4x−.5
0 ≤ 4(0)-.5
0 ≤ -.5
Is zero less than -.5? No. So shade the right side of the green graph.
Now, knowing the solution set for green graph and the red graph, just shade in the sides they have in common.
In this problem, the shaded area should be in the middle of both of the graphs.