SOLUTION: Totally confused please help Given the pair of enequalities, y > x + 1 y

SOLUTION: Totally confused please help Given the pair of enequalities, y > x + 1 y < 3/2 + 3 graph their solution set.

Question 202637: Totally confused please help
Given the pair of enequalities,
y > x + 1
y < 3/2 + 3
graph their solution set.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Since I do not know how to use Algebra.com's software to actually draw the full, correct graph of the solution, I am going to describe the proper graph and provide a graph that is partially complete and partially incorrect.

To start with think of the related equations:
y = x + 1
y = (3/2)x + 3
I hope you would know how to graph these lines. They are both in Slope-intercept form so they should be easy. The first line would be the points where the y-coordinate equals (x+1). The second line would be the points where the y-coordinate equals ((3/2)x + 3). Since the both inequalities are not of the "or equal to" type, we do not want points where the y equals the right side. So the lines of the equations are NOT part of our solution. But, as we will soon see, they do serve as boundaries!

Now let's think about the inequality y < x + 1. This says the y is less than (x + 1). Where do we find lower y values? Up or down? Hopefully you understand that down is where we find lower y values. This means that the solution to y < x + 1 are the points below the line y = x + 1. If this was our only inequality then we would shade the area below the line y = x + 1 and we would be finished.

But we also have the second inequality y > (3/2)x + 3. This says y is greater than ((3/2)x + 3). Using logic like we did above we should know then that the solution to this equation is above the line y = (3/2)x + 3.

So our solution is the points in the area below y = x + 1 and above the line y = (3/2)x + 3.

Here's a step-by-step procedure:

Graph, as a dotted (not solid), line the graph of y = x + 1. (The dotted line indicates that the points are not to be considered part of the solution. If the inequality has been an "or equal to" type, we would use a solid line indicating that the line, where y = ..., is part of the solution.)
Graph, as a dotted (not solid), line the graph of y = (3/2)x + 3
Now we have a graph of two dotted lines. These lines divide the graph into 4 regions. Find and shade the region that is both below the y = x + 1 and above the y = (3/2)x + 3 line. (Only 1 of the 4 regions fit this description.)

Below is a graph which

Has no shading (which is the critical part of the graph),/li>
Has solid lines where you need dotted lines

I'll leave it to you to figure out which line is which.

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