![graphing inequalities on a coordinate plane graphing inequalities on a coordinate plane](https://i.ytimg.com/vi/QvqJfHaYVd0/maxresdefault.jpg)
When a linear inequality is in the form y> or y≥, shade the area above the graph. How do you know when to shade the region above the line or below the line? If the line is dotted, then the points on the line are not included in the solution set. If the line is solid, then the points on the line are included in the solution set. Any point outside of this shaded region are non-solutions. The shaded region of a linear inequality includes all of the points that are solutions to the inequality. Notice that both inequalities have a shaded region and that y>x+1 has a dotted line, while y≥x+1 has a solid line. When you graph a linear inequality, points on the line can be solutions (more on this later) as well as all of the points in the shaded region, which is called the solution set.Īt this point, it should also be noted that, just like inequalities on the number line graphs, there is a difference between the solution sets of ≥/≤ and >////, meaning numbers on the line are not included in the solution set.Įxample: Figure 05 below compares the linear inequalities y>x+1 and y≥x+1.
![graphing inequalities on a coordinate plane graphing inequalities on a coordinate plane](https://media.cheggcdn.com/study/719/7191292e-5df1-4a38-a5b7-606b52c4f4a7/image.png)
Why? When you graph a linear equation, all of the points on the line are solutions to the equation, while all of the points that are not on the line are non-solutions. Notice that the graphs of the equations and the graphs of the inequalities have the same lines, but that the inequality includes shaded region. Key Takeaway: Inequalities can have an infinite amount of possible solutions. You can visualize the solutions to x+5≥8 and x+5>8 on the number line as shown in Figure 02 (the distinction between the solutions of ≥/≤ and >/< inequalities is important to understand before moving forward). The solution x>3 means that any value greater than 3 is a possible solution, but not including 3. This infinite set of values that could be solutions to an inequality is called the solution set.Īdditionally, if we change the inequality from ≥ to > as follows: x+5>8, you can conclude that the solution to the inequality is x>3. And there are an infinite amount of values that satisfy this criteria. The solution x≥3 means the value 3 and any value greater than 3 is a possible solution. What if we change the equation x+5=8 to the inequality x+5≥8? Using algebra, you can conclude that the solution to the inequality is x≥3. Key Takeaway: Equations can have only one possible solution. Using simple algebra, you can figure out that the solution to this equation is x=3 (see Figure 01).įor this equation, 3 is the only possible solution that would make the equation true and all other values would not work (we can these values non-solutions). Let’s start by considering the equation x+5=8. Inequalities: What is the difference? Equations
![graphing inequalities on a coordinate plane graphing inequalities on a coordinate plane](https://quickmath.com/images/artimages/b1c6/chapte18.jpg)
Once you are able to graph a linear equation in y=mx+b form, you are ready to start graphing linear inequalities in y>mx+ b (or y<, y≥, y≤ form).īut first, let’s quickly review some important math concepts and definitions related to linear relationships and inequalities that will help you along the way. If you need a recap of graphing lines in y=mx+b form, we suggest that you review our free Graphing Lines Using Slope step-by-step guide for students. Graphing linear inequalities is similar to graphing linear equations (with a few extra steps) and this pre-requisite knowledge is required. However, before going forward, make sure that you are familiar with graphing linear equations in y=mx+b form where m represents the slope and b represents the y-intercept. Identify the solution set of a linear inequalityīy working through three examples, you will gain experience and understanding of both of these skills. Graph a linear inequality on the coordinate plane By the end of this guide, you will be able to:
![graphing inequalities on a coordinate plane graphing inequalities on a coordinate plane](https://i.ytimg.com/vi/nWm_OAatxpQ/maxresdefault.jpg)
Welcome to this simple and straightforward guide to graphing linear inequalities on the coordinate plane.