# Advanced Geometry : How to graph a two-step inequality

## Example Questions

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

Solve and graph the following inequality:

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:

### Example Question #2 : Graphing

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

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 #3 : Graphing

Which of the following lines is perpendicular to the line ?

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 #291 : Advanced Geometry

Which inequality does this graph represent?

;

;

;

;

Explanation:

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

### Example Question #291 : Advanced Geometry

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

;

Explanation:

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 #1 : How To Graph A Two Step Inequality

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

;

Explanation:

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 #292 : Advanced Geometry

Find the -intercept for the following:

Explanation:

.

.

.

### Example Question #1 : 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?