we are given the inequality
[tex]y+1>2(x-1)[/tex]
To graph this inequality, we first consider the line
[tex]y+1=2(x-1)[/tex]
or equivalently
[tex]y=2(x-1)-1[/tex]
Note that when x=1, we have that y=-1. So the line should pass through the point (1,-1)
Note also that when x=2, we have that
[tex]y=2(2-1)-1=2\cdot1-1=1[/tex]
so it should pass through the point (2,1)
Now, this is about the line. But, we are interested on the inequality
[tex]y>2(x-1)-1[/tex]
This is simply all the points that are located above the line 2(x-1)-1. So, the graph of the region would be
which corresponds to graph A.
