The statement which correctly describes the shaded region for the inequality is 
Further explanation:
In the question it is given that the inequality is  .
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The equation corresponding to the inequality  is
 is  .
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The equation  represents a line and the inequality
 represents a line and the inequality  represents the region which lies either above or below the line
 represents the region which lies either above or below the line  .
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Transform the equation  in its slope intercept form as
 in its slope intercept form as  , where
, where  represents the slope of the line and
 represents the slope of the line and  represents the
 represents the  -intercept.
-intercept.  
 -intercept is the point at which the line intersects the
-intercept is the point at which the line intersects the  -axis.
-axis.  
In order to convert the equation  in its slope intercept form add
 in its slope intercept form add  to equation
 to equation  .
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Now, divide the above equation by  .
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Compare the above final equation with the general form of the slope intercept form  .
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It is observed that the value of  is
 is  and the value of
 and the value of  is
 is  .
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This implies that the  -intercept of the line is
-intercept of the line is  so, it can be said that the line passes through the point
 so, it can be said that the line passes through the point  .
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To draw a line we require at least two points through which the line passes so, in order to obtain the other point substitute  for
 for  in
 in  .
.  


 
  
This implies that the line passes through the point  .
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Now plot the points  and
 and  in the Cartesian plane and join the points to obtain the graph of the line
 in the Cartesian plane and join the points to obtain the graph of the line  .
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Figure  shows the graph of the equation
 shows the graph of the equation  .
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Now to obtain the region of the inequality  consider any point which lies below the line
 consider any point which lies below the line  .
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Consider  to check if it satisfies the inequality
 to check if it satisfies the inequality  .
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Substitute  and
 and  in
 in  .
.  
 
  

The above result obtain is not true as  is not greater than
 is not greater than  so, the point
 so, the point  does not satisfies the inequality
 does not satisfies the inequality  .
.  
Now consider  to check if it satisfies the inequality
 to check if it satisfies the inequality  .
.  
Substitute  and
 and  in the inequality
 in the inequality  .
.  
 
  
 
  
 
  
The result obtain is true as  is greater than
 is greater than  so, the point
 so, the point  satisfies the inequality
 satisfies the inequality  .
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The point  lies above the line so, the region for the inequality
 lies above the line so, the region for the inequality  is the region above the line
 is the region above the line  .
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The region the for the inequality  does not include the points on the line
 does not include the points on the line  because in the given inequality the inequality sign used is
 because in the given inequality the inequality sign used is  .
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Figure  shows the region for the inequality
 shows the region for the inequality  .
.
Therefore, the statement which correctly describes the shaded region for the inequality is 
Learn more:  
- A problem to determine the range of a function brainly.com/question/3852778
- A problem to determine the vertex of a curve brainly.com/question/1286775
- A problem to convert degree into radians brainly.com/question/3161884
Answer details:
Grade: High school
Subject: Mathematics  
Chapter: Linear inequality
Keywords: Linear, equality, inequality, linear inequality, region, shaded region, common region, above the dashed line, graph, graph of inequality, slope, intercepts, y-intercept, 6y-3x=9, 6y-3x>9, slope intercept form.