graph the inequality in the coordinate plane

GRAPH THE INEQUALITY IN THE COORDINATE PLANE HOW TO
GRAPH THE INEQUALITY IN THE COORDINATE PLANE FREE

Graphing systems of inequalities will become easer for you after working on a few examples. Examples of solutions to the system of inequalities would be the points (0,0), (-2,2 ), and (-4,-1), since they are all in the solution set region, which is labeled with an ‘S'.”Īre you confused? That’s okay for now. However, for the system of linear inequalities, you can see that all of the points in the overlapping shaded regions can be solutions and there are infinitely many of them. In Figure 05 below, you can see that the one and only solution to the system of linear equations is the intersection point (5,2). A solution set will have infinitely many points, all of which satisfy every inequality in the system of inequalities. When solving systems of linear equations, the solution is a point that satisfies all the equations in the system, but for systems of inequalities, it is an entire region on the coordinate plane. Graphing Systems of Inequalities: The Solution Set If you can graph a single linear inequality, then you are ready to start graphing systems of inequalities. Points on the line are only included if the line is solid.įigure 04 below recaps both solid and dashed lines and when to shade above a line and when to shade below. All of the points in this region will be solutions to the inequality. When an inequality is in the form y< or y≤, you must shade the region below the graph. Points on the line are only included if the line is solid. When an inequality is in the form y> or y≥, you must shade the region 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. All of the points in the non-shaded region are non-solutions. The shaded region includes all of the points that are solutions to the inequality (there are infinitely many of them). Next, letss recap the meaning of the shaded region on the graph of any linear inequality. Shaded Regions when Graphing Inequalities: Also notice that y≥x+1 has a solid line while y>x+1 has a dotted line. Notice that the equation does not have a shaded region while both inequalities do have a shaded region. This means that numbers on the line are not included in the solution set.įor example, Figure 03 below shows the difference between the equation y=x+1 and the inequalities y>x+1 and y≥x+1.

GRAPH THE INEQUALITY IN THE COORDINATE PLANE HOW TO

There are a couple of notations that you will need to know before we can start graphing systems of inequalities.įor starters, lets recap how to graph a single linear inequality of the form y>, y≥, y. Standard Notations used for Graphing Systems of Inequalities Keeping this in mind will greatly help you to understand graphing and solving linear inequalities. The key difference between an equation and an inequality is that an equation has only one solution, while an inequality has a solution set with infinitely many solutions. The inequality x≥7 means that x can equal 7 or any value greater than 7. Inequalities have an infinite number of solutions (this collection of possible solutions is called a solution set). We can visualize the equation x=7 on the number in Figure 01 below: What is the difference between an equation and an inequality?ĭefinition: An equation is a mathematical statement showing that two expressions are equal using the sign: =Īn example of an equation is x=7 where x equals 7 (and only 7). If you already know how to graph a system of equations, you are ready to follow this step-by-step guide that will teach you everything yoy need to know about graphing systems of linear inequalities.īefore we dive into solving systems of inequalities, let’s review some definitions and learn the standard notations used when graphing systems of inequalities.

GRAPH THE INEQUALITY IN THE COORDINATE PLANE FREE

If you are not confident in your ability to graph and solve a system of linear equations we suggest that review our free Solving Systems of Equations guide. However, it is important to note that graphing systems of inequalities involves a graphical approach that you may not have explored before. In math, once you have learned how to graph and solve a system of linear equations, you are ready to take the next step and learn two new important algebra skills:

Graph the inequality in the coordinate plane