Advanced Geometry : How to graph a two-step inequality

Example Questions

Example Question #1 : Graphing

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 #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?      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 #1 : 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 #201 : Coordinate 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 #202 : Coordinate 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 #203 : Coordinate Geometry

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 #204 : Coordinate 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?        