GMAT Math : Graphing

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #3 : Graphing A Two Step Inequality

Capture2

Which of the following inequalities is graphed above?

Possible Answers:

None of the above.

Correct answer:

Explanation:

In order to graph the inequality pictured above, we must first find the equation of its boundary line. Based on the image, we see that the line includes the points  and , so the slope of the line is

.

We can now find the -intercept form of the line by substituting  and the point   into the slope-intercept equation  and solving for :

The equation of the boundary line is therefore . Since we see that the boundary line is solid, we know that the values on the line are included in the inequality, so the  sign will be replaced by a  or a .

In order to determine which one, we can test a point in the solution set; let's test  :

 _____

 _____

 _____

, so the correct symbol is 

Example Question #4 : Graphing A Two Step Inequality

Capture3

Which of the following inequalities is graphed above?

Possible Answers:

None of the above.

Correct answer:

Explanation:

In order to graph the inequality pictured above, we must first find the equation of its boundary line. Based on the image, we see that the line includes the points  and , so the slope of the line is

.

We can now find the -intercept form of the line by substituting  and the point   into the slope-intercept equation  and solving for :

The equation of the boundary line is therefore . Since we see that the boundary line is dashed, we know that the values on the line are excluded from the inequality, so the  sign will be replaced by a  or a .

In order to determine which one, we can test a point in the solution set; let's test  :

 _____

 _____

 _____

, so the correct symbol is 

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