How to graph a two-step inequality

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Geometry › How to graph a two-step inequality

Questions 1 - 8
1

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?

Explanation

Inequality_region1

2

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:

Number_line

3

Which inequality does this graph represent?

Inequality a

;

;

;

Explanation

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

4

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

;

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 .

5

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 .

6

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

;

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.

7

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:

8

Find the -intercept for the following:

Explanation

.

.

.

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