Question

Which of the following is the graph of the inequality y+1>2(x-1)?BCD(2.1)(31)(3.1)(2.0)55(1.1)51 (2-1)(2.-1)(1.-2)A. Graph AB. Graph BC. Graph CD. Graph D

Answer 1

we are given the inequality

`y+1>2(x-1)`

To graph this inequality, we first consider the line

`y+1=2(x-1)`

or equivalently

`y=2(x-1)-1`

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

`y=2(2-1)-1=2\cdot1-1=1`

so it should pass through the point (2,1)

Now, this is about the line. But, we are interested on the inequality

`y>2(x-1)-1`

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.