we have graphed the boundary line for the linear inequality. Determine the
correct half-plane in each case, and complete the graph. 
Y > 3
THE GRAPH THAT IS ON THE BOOK ITS A LINE JUST GOING THROUGH ALL 3 ON THE TOP
TWO THE NEGATIVE SIDE AND POSITIVE SIDE LIKE THIS: 
<----------3------------------> 
i DON'T KNOW HOW TO ANSWER THIS AND I DON'T EVEN UNDERSTAND WHAT IS ASKING


A "half-plane" is all the area on just one side of a line.

The boundary line for the INEQUALITY 

y > 3

has the EQUATION

y = 3


To draw the graph of y = 3, plot some points.  Since there is only
one letter in y = 3, we must choose the y-value of every point to
be 3, but since there is no x, you can choose x to be any number.
I'll arbitrarily pick 3, -2, 5, and -4 for x, and only 3 for y.

 x|y
-----
 3|3
-2|3
 5|3
-4|3

So plot these points (3,3), (-3,3), (5,3), and (-4,3)

They all line on this horizontal line:



That horizontal line should be drawn dotted, not solid
as I have here, but I can only draw solid lines on here,
but you can draw it dotted on your paper.  (If the
inequality symbol is > or <, then you draw the boundary
line dotted.  If the inequality symbol is > or
<, you draw the boundary line solid.

If the inequality starts off " y > " or " y > " 
you shade the area ABOVE the line. 

If the inequality starts off " y < " or " y < "
you shade the area BELOW the line.

Your inequality starts off " y > ", so you shade the
area ABOVE the line, like where these slanted lines are



But don't forget to draw the horizontal line dotted instead of
solid as I have it here, and to shade the area ABOVE the line.

The area you shade is called a "half plane"

Edwin