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Example Questions
Example Question #3 : Graphing A Two Step Inequality
Which of the following inequalities is graphed above?
None of the above.
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
Which of the following inequalities is graphed above?
None of the above.
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 :