Advanced Geometry : How to graph a two-step inequality

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

Example Question #1 : How To Graph A Two Step Inequality

Solve and graph the following inequality:

Possible Answers:

Correct answer:

Explanation:

To solve the inequality, the first step is to add  to both sides:

 

The second step is to divide both sides by :

To graph the inequality, you draw a straight number line. Fill in the numbers from  to infinity. Infinity can be designated by a ray. Be sure to fill in the number , since the equation indicated greater than OR equal to.

The graph should look like:

Number_line

Example Question #1 : How To Graph A Two Step Inequality

Points  and  lie on a circle. Which of the following could be the equation of that circle?

Possible Answers:

Correct answer:

Explanation:

If we plug the points  and  into each equation, we find that these points work only in the equation . This circle has a radius of  and is centered at .

Example Question #2 : Graphing

Which of the following lines is perpendicular to the line ?

Possible Answers:

Correct answer:

Explanation:

The key here is to look for the line whose slope is the negative reciprocal of the original slope.

In this case,  is the negative reciprocal of .

Therefore, the equation of the line which is perpendicular to the original equation is:

Example Question #1 : How To Graph A Two Step Inequality

Which inequality does this graph represent?

Inequality a

Possible Answers:

;

;

;

Correct answer:

;

Explanation:

The two lines represented are and . The shaded region is below both lines but above 

Example Question #2 : How To Graph A Two Step Inequality

What is the area of the shaded region for the following inequality:

;

Possible Answers:

Correct answer:

Explanation:

This inequality will produce the following graph:

Inequality a

The shaded area is a triangle with base 7 and height 2.

To find the area, plug these values into the area formula for a triangle, .

In this case, we are evaluating , which equals 7.

Example Question #3 : How To Graph A Two Step Inequality

What is the area of the shaded region for this system of inequalities:

;

Possible Answers:

Correct answer:

Explanation:

Once graphed, the inequality will look like this:

Inequality b

To find the area, it is easiest to consider it as 2 congruent triangles with base 6 and height 3.

The total area will then be

, or just .

Example Question #2 : How To Graph A Two Step Inequality

Find the -intercept for the following:

Possible Answers:

Correct answer:

Explanation:

 

.

.

.

Example Question #4 : How To Graph A Two Step Inequality

Let D be the region on the (x,y) coordinate plane that contains the solutions to the following inequalities:

, where  is a positive constant

Which of the following expressions, in terms of , is equivalent to the area of D?

Possible Answers:

Correct answer:

Explanation:

  Inequality_region1

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