SOLUTION: In Exercise 8, the text provides a graph of the boundary line for the given linear inequality. Determine the correct half-plane, and complete the graph. Examples 1 and 2 on pp 63

Algebra ->  Linear-equations -> SOLUTION: In Exercise 8, the text provides a graph of the boundary line for the given linear inequality. Determine the correct half-plane, and complete the graph. Examples 1 and 2 on pp 63      Log On


   

Question 88523: In Exercise 8, the text provides a graph of the boundary line for the given linear inequality. Determine the correct half-plane, and complete the graph. Examples 1 and 2 on pp 638-639 provide the best illustration of what’s expected.
y > 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph y%3E3, we need to graph the equation y=3 (just replace the inequality sign with an equal sign).
So lets graph the line y=3 (note: if you need help with graphing, check out this solver)

+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+3%29+ graph of y=3
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality y%3E3 with the test point

Substitute (0,0) into the inequality
%280%29%3E3 Plug in x=0 and y=0
0%3E3 Simplify

Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of y%3E3 with the boundary (which is the line y=3 in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)