### All Advanced Geometry Resources

## Example Questions

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

Solve and graph the following inequality:

**Possible Answers:**

**Correct answer:**

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:

### Example Question #2 : 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:**

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 #3 : How To Graph A Two Step Inequality

Which of the following lines is perpendicular to the line ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

;

;

;

**Correct answer:**

;

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:**

This inequality will produce the following graph:

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:**

Once graphed, the inequality will look like this:

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 #4 : How To Graph A Two Step Inequality

Find the -intercept for the following:

**Possible Answers:**

**Correct answer:**

.

.

.

### 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:**

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