How to Graphing Inequalities in the Coordinate Plane.

Objective:

• Graph inequalities in a xy coordinate graph.
  

Assumptions:

• Ability to graph a line using the slope-intercept form (y = mx + b)

Concepts:

• The shaded area of a graph represents all of the coordinates that will work in a given equation.
  
• A solid edge of the shaded area means that the edge is part of the solutions to the equation.
  
• A dashed edge of the shaded area means that the edge of the graph is not part of the solutions.
  

Directions:
Graph the equation
Step 1: Draw the graph just as you would y = x . This equations in slope intercept form would look like this . The 0 means that you will go through the origin, place a point there. Now use the slope to draw the rest of the line. From the origin go up one and to the right one and place another point. Repeat until you have several points.

Now draw a solid line because the equation to be graphed is greater than or equal to. Your graph should now look like this:

Step 2: Next shade everywhere above the line because the equation states that the y values are greater than or equal to the line for any given x value.

Now check your answer by inserting a couple of points from the shaded area and non-shaded area.

Shaded

Does the point ( 1, 2) work in the equation? yes
Does the point ( -1, 0) work in the equation? yes

Non-shaded

Does the point ( 1, 0) work in the equation? no
Does the point ( 2, 1) work in the equation? no


Lets try another one.

Graph graph y > 2x + 3
Remember the steps: plot some points, draw the line (solid if equal to, dashed if greater than or less than), shade above with greater than, shade below with less than.

The line will cross the y axis as 3 then go up 2 and over 1 for the slope. Start by placing a point at 3 on the y axis. Next use the slope to place 2 more dots, then make a dashed line through the dots.

The equation uses the greater than inequality so it should be shaded above the line.

Now that we have the common ones out of the way lets look at the ones that may trip you up such as the ones with only one variable like y > 2 and x < -3.

Graph y > 2

Remember that is just a horizontal line. This is just a horizontal line that is shaded above the line and dashed because it is not equal to the line it is only greater than the line.

Graph x < -3

Remember that is just a vertical line. This is just a vertical line that is shaded to the left of the line and dashed because it is not equal to the line it is only less than the line. The x values on the left are less than the line.

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Things to remember when graphing inequalities:

≥ Solid line and shaded above the line.

≤ Solid line and shaded below the line

> Dashed line and shaded above the line

y > # Horizontal line and shaded above the line

y < # Horizontal line and shaded below the line

x > # Vertical line and shaded on the right side of the line

x < # Vertical line and shaded on the left side of the line.

Student Line Grapher

While working with my Algebra 1 students to try and teach them how to graph lines. I came up with the idea to create a flash module that would work with moodle to record student's graphs. This idea came out of my previous project which was to create a quick way to draw graphs while lecturing.

This module is pretty slick you can use it to teach students how to graph linear inequalities and equality graphs. My other web page explains the details but here are the basics.

Select your line type, which is by default solid for equality next click to points that are on the line. The flash module extends the line to the edge of the graph. If you are going to graph an inequality then click on shading. Click to points on the line and then which side of the line should be shaded.

You will notice that when you select shading you now have the option of two different line types. The dashed line is for inequality graphs.

Here is the really cool part though. When you create the graph, if you set a value in the flashvars variable the equation of the line can be recorded to a form value in the web page which can then be submitted for grading.

I've implemented this version with moodle but I'll post that information later since I'm not using the latest version of moodle and want to cleaned up the code a little bit and make sure that it is compatible with the latest version.