# Graphing and writing inequalities

A system of inequalities is two or more inequalities that pertain to the same problem. Graphing Inequalities Graphing inequalities is very similar to graphing linear equations. Once your linear equation is graphed, you then must focus on the inequality symbol and perform two more steps. It's pretty easy and fun. Stick with me and you'll have no problems by the end of this lesson. This is a graph for a linear inequality. Notice how we have a boundary line that can be solid or dotted and we have a half plane shaded.

These are the two extra steps that you must take when graphing inequalities. In order to succeed with this lesson, you will need to remember how to graph equations using slope intercept form.

## Inequalities Worksheets | Math Worksheets

There Graphing and writing inequalities be two additional steps that you must take when graphing linear inequalities. As shown in this image, the first step will be to determine whether you will use a solid boundary line or a dashed boundary line.

The inequality symbol will help you to determine the boundary line. If the inequality symbol is greater than or less than, then you will use a dotted boundary line.

This means that the solutions are NOT included on the boundary line. If the inequality symbol is greater than or equal to or less than or equal to, then you will use a solid line to indicate that the solutions are included on the boundary line.

The second step will be to determine which half plane to shade. If this all sounds confusing, don't worry Take a look at the examples below and it will all make sense.

## Writing Logarithmic Equations from Points and Graphs

You may want to keep this handy for a reference. Example 1 - Graphing Inequalities Graph the inequality: Graph the inequality as you would a linear equation.

Remember to determine whether the line is solid or dotted. The points on the line are NOT solutions! Determine which side of the line contains the solutions.

Since y is less than the expression, you will shade below the line. If you are unsure of which side to shade, pick any point on the graph that's not on the line. You are choosing a test point to determine which side contains the solutions. I will choose 0,0 because this is the easiest point to substitute into the inequality to check for solutions. Since 0,0 is a solution and is to the right of the line, ALL of the points to the right of the line are solutions!

Therefore, we will lightly shade the area to the right of the line to show that this side of the line contains all of the solutions to the inequality. Shade the side of the line that contains the solutions to the inequality. Did you notice how our boundary line was a dotted line because of the less than symbol that was used in the inequality?

Also, you may have realized that you shade below the dotted line because of the less than symbol in the inequality. However, if you are unsure you can always choose a test point. I always use the point 0,0 if it's not on the line. Substitute 0,0 into the original inequality. If the math sentence is true once you substitute 0,0then that means that 0,0 is a solution and you shade the half plane that contains 0,0.

If the math sentence is false when you substitute 0,0then that means that 0,0 is not a solution and the other half plane or the side of the line that does not contain 0,0 should be shaded. For this second example, we'll need to rewrite the equation so that it's in slope intercept form before we graph.

Also take note that the sign is greater than or equal to, so we will graph a solid line this time instead of a dotted line. This example will also demonstrate how to choose three solutions to the inequality. Rewriting the Inequality in Slope Intercept Form.This page will help you draw the graph of a line.

It assumes the basic equation of a line is y=mx+b where m is the slope and b is the y-intercept of the line. In order to succeed with this lesson, you will need to remember how to graph equations using slope intercept form..

There will be two additional steps that you must take when graphing linear inequalities. There are a few pieces of information that you have to put together in order to create a graph of a quadratic function.

Before anything, though, we need to learn the standard form of a quadratic and this is it: \(ax^2 + bx + c\) a,b,and.

This page will help you draw the graph of a line. It assumes the basic equation of a line is y=mx+b where m is the slope and b is the y-intercept of the line. Kindergarten Worksheets Writing Numbers Worksheet. This Kindergarten Worksheet will produce worksheets for practicing writing numbers between 0 and 9.

There are a few pieces of information that you have to put together in order to create a graph of a quadratic function. Before anything, though, we need to learn the standard form of a quadratic and this is it: \(ax^2 + bx + c\) a,b,and.

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