# what is the boundary line in inequalities

Select a subject to preview related courses: The line y = x + 1 is the boundary line and the solution for the inequality is anything under the line. Remember from the module on graphing that the graph of a single linear inequality splits the coordinate plane into two regions. Notice that the line is actually dotted, that means that points on the line itself are not actually included in the graph. Notice that the black line is the boundary line, or perimeter, of this yellow triangle. If the boundary line is solid, then the linear inequality must be either ≥ or ≤. Hang in there, a lot of the steps are concepts from the past, things you should already have seen and done before. All points on the left are solutions. 0 ≥ 8. courses that prepare you to earn Let's look at each in turn to get a better understanding of boundary lines and how they work. Refer to the explanation. This indicates that any ordered pair in the shaded region, including the boundary line, will satisfy the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥. You have a big yard, but no fence. Earn Transferable Credit & Get your Degree. Examples: y>3x/4, x =2, y>=1, y>-2x Inequality: Step 1: Find the equation of the boundary line. When you graph an equation, you get a line. A linear inequality describes an area of the coordinate plane that has a boundary line. If the boundary line is solid, then the inequality sign is either ≥ or ≤. Stick with me and you'll have no problems by the end of this lesson. The line is solid with a y-intercept at (0.-2) and slope of B. | {{course.flashcardSetCount}} Since the boundary line is graphed with a solid line, the inequality includes the equal sign. The shaded region shows the solution of the inequality . Two worked-out examples showing how to graph inequalities that have horizontal or vertical boundary lines. If the boundary line is dotted, then the inequality sign is either > or <. Both boundary lines are solid because the inequalities are inclusive. The line with equation is the boundary line that separates the region where from the region where. Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level. when the boundary is included into a solution. As we’ve done in previous questions, select a point that is not on the first boundary line to determine which side of the line to shade. The graph shows the inequality . The half-plane that is a solution to the inequality is usually shaded. Share on Facebook. What are the attributes of the boundary line of this inequality?-3x - 2y <6 A. Every ordered pair in the shaded area below the line is a solution to y<2x+5y<2x+5, as all of the points below the line will make the inequality true. The Boundary line defines the space or area. (Recorded on a … Why are the boundary lines for two- variable inequalities with greater than and less represented by dotted lines? Step 3: Now graph the y = x + 1. y=2x-1 Substitute 0 for y. Not sure what college you want to attend yet? Solid boundary line: < or > If the problem includes where it is equal, then you will have a solid boundary line. The dashed line is y=2x+5y=2x+5. We can notice that the line y = - 2x + 4 is included in the graph; therefore, the inequality is y = - 2x + 4. The linear inequality divides the coordinate plane into two halves by a boundary line the line that corresponds to the function. Consider the graph of the inequality y<2x+5y<2x+5. 0=2x-1 Add 1 to both sides. Y-intercept: value of y when x=0 Substitute 0 for x. y=2(0)-1 y=-1 The y-intercept is (0,-1) Plot the points. when the boundary line is not included into a solution. If we are given a strict inequality, we use a dashed line to indicate that the boundary is not included. Some of these problems may get a little long. We can explore the possibilities of an inequality using a number line. credit by exam that is accepted by over 1,500 colleges and universities. In this inequality, the boundary line is plotted as a dashed line. In simpler speak, a linear inequality is just everything on ONE side of a line … x + y 2 dashed solid Weegy: Not enough information there. There is a boundary line for each and every shape. If you graph an inequality on the coordinate plane, you end up creating a boundary. 0:20. The boundary line is the line y = 4x − 5.5, and it is dashed because our y term is “greater than,” not “greater than or equal to.” To identify the bounded region, the region where the inequality is true, we can test a couple of coordinate pairs, one on each side of the boundary line. X-intercept: value of x when y=0 Substitute an equal sign for the less than symbol. Jon Anderson 4,450 views. open half plane. Since the dependent variable is isolated in the left expression, and the inequality sign includes <, shade the area the boundary line. Graph the inequality . This could be a geometric shape or an inequality graph. Perimeter is a boundary line measure commonly used with shapes. There are three steps: Rearrange the equation so "y" is on the left and everything else on the right. What are the attributes of the boundary line of this inequality?-3x - 2y <6 A. If you can remember it you’ll always be able to solve these kinds of inequalities. Every point in that region is a solution of the inequality. 5 | 1.3 Determine and explain the solution region that satisfies a linear inequality, using a test point when given a boundary line. Services. sign does not include the possibility of equality and the solution set is continuous. OPEN ENDED Create an absolute value inequality in which none of the possible solutions fall in the second or third quadrant. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>) Shade above the line for a … The solution is the region where the shading overlaps. The boundary line divides the coordinate plane in half. Here is the graph of the first inequality where the boundary line is solid and the shaded area is found below it. The graph of will be a dotted boundary line with shaded the area found under it. It's pretty easy and fun. Because it’s the easiest to evaluate. Shade in the side of the boundary line where the inequality is true. Notice how we have a boundary line that can be solid or dotted and we have a half plane shaded. This indicates that any ordered pair that is in the shaded region, including the boundary line, will satisfy the inequality. There is a fairly simple process to solving these. The inequality is expressed in slope-intercept form in level 1 and has to be converted to slope-intercept form in Level 2. Graphing Linear Inequalities. Weak inequalities include "or equal to". Step 2: Change inequality to equality. You would probably put the dog on a leash and walk him around the edge of the property. <=, >= If the boundary line is dotted, then the linear inequality must be either > or <> In essence, when you do boundary training with your dog, you are walking the perimeter of your property. For the inequality, the line defines the boundary of the region that is shaded. Your email address will not be published. Yes, if it is a true equation with an equal sign the graph will result in a line of some sort. The resulting values of x are called boundary points or critical points. Tags: Question 11 . All other trademarks and copyrights are the property of their respective owners. Learning Objectives. The inequality solver will then show you the steps to help you learn how to solve it on your own. Graph the boundary line. Let's pretend you just got a new dog. If the inequality had been y ≤ 2x + 5, then the boundary line would have been solid. ... polynomial inequality by boundary method - Duration: 6:36. sharon weltlich 1,989 views. If the inequality is ≤ or ≥, ≤ or ≥, the boundary line is solid. To solve your inequality using the Inequality Calculator, type in your inequality like x+7>9. Step 2: Change inequality to equality. The origin is the point (0, 0). <, > On the other hand, a continuous line with no breaks means the inequality does include the boundary line. Tags: ... y > 8. y < 8. The boundary line is dotted/dashed is the inequality includes only < or >; however, if or equal to is included, the line is drawn solid and points on the line are included in the solutions. If you doubt that, try substituting the x and ycoordinates of Points A an… Any point you choose on the left side of the boundary line is a solution to the inequality y > x + 4 y > x + 4. All of the points in the yellow shaded area are solutions to this inequality. the graph of a compound inequality containing OR; the solution is a solution of either inequality, not necessarily both boundary a line or curve that separates the coordinate plane into regions 1/2=x The x-intercept is (1/2,0). tracey111005|Points 20| User: The inequality 2x - 3y 5 is satisfied by point (, ).True False Weegy: The answer is "False" bongche|Points 3864| User: The inequality x - y > 0 is satisfied by point (-1, 1). That means the equation can only be using either of the first two symbols. boundary. Don't let that discourage you, you can do it. Q. This is because the inequality includes a symbol that means greater than or equal to, instead of just greater than. If the inequality symbol is greater than or equal to or less than or equal to , then you will use a solid line … first two years of college and save thousands off your degree. All points above the boundary line are solutions. A boundary line, which is the related linear equation, serves as the boundary for the region.You can use a visual representation to figure out what values make the inequality true—and also which ones make it false. Study.com has thousands of articles about every The inequality x ≥ –3 will have a vertical boundary line. To find the perimeter (boundary line) of a shape, just add up the length of all the sides. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Check by choosing a test point. Systems of nonlinear inequalities can be solved by graphing boundary lines. Graph Inequalities with a Boundary through the Origin - Duration: 3:15. How to Graph a Linear Inequality. This lesson reviews the definition of boundary lines and gives examples of boundary lines for both shapes and inequality graphs. In this case, it was dashed because points on the line don’t satisfy the inequality. divided from the coordinate plane into two. The second inequality will have a solid boundary line and shaded area is found above it. Create an account to start this course today. Why did we choose ? How many times has meghan markle been married www cbs young and the restless com video, Graphing linear inequalities (Pre-Algebra, Graphing and functions) � Mathplanet, Your email address will not be published. Sciences, Culinary Arts and Personal See Figure 4.33. Enrolling in a course lets you earn progress by passing quizzes and exams. Then, describe what the boundary line can tell us about solutions to an inequality. This line is called the boundary line (or bounding line). In addition, since the original inequality is strictly greater than symbol, \Large{\color{red}>}, we will graph the boundary line as a dotted line. For the inequality, the line defines one boundary of the region that is shaded. The line is solid with a y-intercept at (0.-3) and slope of - 0 C. The line is dashed with a y-intercept at (0.-2) and slope of D. The line is dashed with a … When you are graphing inequalities, you will graph the ordinary linear functions just like we done before. I drew a dashed green line for the boundary since the . Did you know… We have over 220 college All rights reserved. I shaded the half plane that included (0, 0), since 8 (0, 0) is a solution to the linear inequality. Dashed lines are used for "strict" inequalities. In inequalities, an algebraic expression stating that two values are not the same, the graph of the line (as if it were an equation) creates the boundary line for solutions of the inequality. cecilpolk4 is waiting for your help. Should I Major in Math? Every inequality has a boundary line, which is the equation produced by changing the inequality relation to an equals sign. SURVEY . To see that this is the case, choose a few test points 66 and substitute them into the inequality. ... Boundary Line - Visualizing Algebra - Duration: 0:20. Test a point that is not on the boundary line. This indicates that any ordered pair in the shaded region, including the boundary line, will satisfy the inequality. If they didn’t, the boundary line would be dashed and the inequality the inequality would be . Which of the following inequalities matches the given graph? Provide examples. The trick is knowing where to shade (up or down, left or right). Any point you choose above the boundary line is a solution to the inequality y > x + 4. y > x + 4. Are the points on the boundary line part of the solution set or not? If you were to look down at your property from a bird's eye view, you would see a geometric shape. Since (0) is greater than (0) -3, or 0 is greater than -3, is a true statement, the side of the line that contains the point (0, 0) is shaded. Anyone can earn The line is solid with a y-intercept at (0.-3) and slope of - 0 C. The line is dashed with a y-intercept at (0.-2) and slope of D. The line is dashed with a y-intercept at (0.-B) and slope of - See answer avavjones is waiting for your help. Find y(\pi), given the initial value problem xy' = 2y + x^{3} \cos x, where y(\pi / 2) = \pi^{2} / 4. In other words, if you have < or >, you will have a solid line for your boundary line. Now were are ready to graph each one of them. The examples of boundary lines in math are given below. If they did, as they would have if the inequality had been y ≤ 2x + 5, then the boundary line would have been solid. Boundary Line - Visualizing Algebra - Duration: 0:20. Visit the Geometry for Kids page to learn more. In this case, it is shown as a dashed line as the points on the line don’t satisfy the inequality. Notice that we used a solid boundary line since the inequality symbol is "less than or equal to" in this problem. The line is solid with a y-intercept at (0.-2) and slope of B. Step 1: Get a zero on one side of the inequality.It doesn’t matter which side has the zero, however, we’re going to be factoring in … Step 2: Graph the boundary line for the inequality . If you need help how to graph vertical and horizontal lines, check it out on this separate lesson. Graphing Inequalities To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. Required fields are marked *, How to find the boundary line of an inequality. Since this inequality is not true, we do not shade the entire region that contains (0,0). Udacity 137 views. the graph of at least one of the inequalities. Example 1: Write the inequality that represents this graph. Plot the boundary points on the number line, using closed circles if the original inequality contained a ≤ or ≥ sign, and open circles if the original inequality contained a < or > sign. One side of the boundary line contains all solutions to the inequality. Create your account, Already registered? imaginable degree, area of No, they are NOT part of the solution set . Is it a solution of the inequality? union. In this tutorial, you'll learn about this kind of boundary! Before graphing a linear inequality, you must first find or use the equation of the line to make a boundary line. You want to teach the dog how to stay in your yard and not run out in the street or into your neighbor's property. The green line that marks the edge of the bounded area is very logically called the and in your case it is a line . This is sufficient in simple situations, such as inequalities with just one variable. Here, the origin is not on the line, so plug the point (0, 0) into the equation, y ≥ −x + 8. y ≥ −x + 8. The solutions for a linear inequality are in a region of the coordinate plane. - Quiz & Self-Assessment Test, Universities with Master's Degrees in Math: How to Choose, Learn Math in the Blogosphere: 10 Top Math Blogs, White House Announces New Math and Science Achievement Campaign, How to Skip the \$100 Graphing Calculator for Your Math Class, Register for the 2010 American Math Challenge, Online Nursing Home Administrator Course and Certification Information, Respiratory Therapist Advancement Opportunities, Earning Your Rhode Island High School Diploma, Seventh-day Adventist Colleges and Universities, Biomedical Engineering Masters Programs in Boston, Overview of Geometry for Elementary School, What is a Boundary Line in Math? It will start out exactly the same as graphing linear equations and then we get to color in the region of the coordinate system that correlates with the inequality. For each and every shape we can determine the area. This boundary cuts the coordinate plane in half. You can choose any point in this area, substitute those values for x and y into the original inequality, and end up with a true math statement. Every day, you would walk the dog around the edge of the property multiple times teaching him how far he is allowed to go. Less Than Or Equal To. Start studying Linear Inequalities, Linear Inequalities with Boundary Lines. To unlock this lesson you must be a Study.com Member. First, define a boundary line and tell where it comes from. Solving linear inequalities is almost exactly like solving linear equations. If the inequality is < or >, < or >, the boundary line is dashed. 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What's a Boundary? Similarly, all points on the right side of the boundary line, the side with (0, 0) (0, 0) and (−5, −15) (−5, −15), are not solutions to y > x + 4 y > x + 4. Since the inequality ≤ sign contains an equal bar, the boundary line is a solid line and any points on the boundary line are included in the solution set. Therefore, y > x + 1 becomes y = x + 1. If the inequality symbol is greater than or less than, then you will use a dotted boundary line. The graph of the line, as if it is an equation, is the boundary line for the inequality. Linear inequalities can be graphed on a coordinate plane.The solutions for a linear inequality are in a region of the coordinate plane. User: For the following inequality, indicate whether the boundary line should be dashed or solid. STEP 3. Boundary lines in math are the same, they identify the outer edge (or outline) of a shape or area. half pane. To solve your inequality using the Inequality Calculator, type in your inequality like x+7>9. As the boundary line in the above graph is a solid line, the inequality must be either ≥ or ≤. Each line plotted on a coordinate graph divides the graph (or plane) into two half‐planes. You are correct that it is a solid line. 60 seconds . Describe the boundary lines for two- variable inequalities. Solid lines are used for "weak" inequalities. First, graph the "equals" line, then shade in the correct area. Last, we must determine if the intersection point of the boundary lines should be included in our solution set of the system of linear inequalities. Likewise, the equation uses one of the last two symbols. Log in here for access. For the following inequality - b + g ≤ 30 - describe the boundary line. The linear inequality divides the coordinate plane into two halves by a boundary line (the line that corresponds to the function). Search Pre-Algebra All courses. answer choices . This boundary is either included in the solution or not, depending on the given inequality. In this case, all points on the line do satisfy the inequality. This tells us that all the boundary lines will be solid. To see that this is the case, choose a few test points and substitute them into the inequality. where the graphs of the two inequalities over lap. line. Inequalities come up all the time when you're working algebra problems. Step 3. Next, graph each inequality with solid boundary lines, as all the inequalities contain greater than or equal to or less than or equal to signs. P = 500 + 500 + 700 + 700 = 2400 ft, {Hint: Remember that a rectangle has four sides and opposite sides are equal; that's why we have two 500's and two 700's. {{courseNav.course.topics.length}} chapters | The boundary line lies instantly inside the boundary. study Learning Objective s. Linear inequalities can be graphed on a coordinate plane. When you did boundary training with your dog, you walked around the edge of your property line. A linear inequality divides a plane into two parts. Therefore, y > x + 1 becomes y = x + 1. Once your linear equation is graphed, you then must focus on the inequality symbol and perform two more steps. Solution: Remembering that boundary line and perimeter are the same thing, we find the perimeter by adding up all the sides. I used green shading to show a continuous solution region. Learning Objective. The line that marks the edge of the bounded area is very logically called the boundary line. 0 ≥ −0 + 8. and career path that can help you find the school that's right for you. We use inequalities when there is a range of possible answers for a situation. On the other side, there are no solutions. 5. The inequality y > –1 will have a horizontal boundary line. The boundary line indicating an edge of something. For the inequality, the line defines the boundary of the region that is shaded. Problem 2. If the inequality is ≤ or ≥, graph the equation as a solid line. The boundary line is a transformation of the graph of XQLWVWR the left. 's' : ''}}. This line divides the xy - plane into two regions: a region that satisfies the inequality, and a region that does not. A boundary line , which is the related linear equation, serves as the boundary for the region. Add your answer and earn points. The intersection of the graphs of the solution sets of the two half-planes is in brown. A linear inequality is a sentence in one of the following forms:. Right? Since the inequality states the y must be greater than or equal to x – 5 the . For example, the equation y = x will be a straight line stretching from the bottom right to the top left corners of the graph, like this: But, when you have an inequality the two sides of the mathematical sentence are not always the same value and the graph often ends up looking like a line with a shaded area. 62/87,21 Graph the inequality . Its equation is x = -1. In this lesson, we saw that a boundary line is the outer edge of a shape or area. Get access risk-free for 30 days, The difference is that the solution to the inequality is not the drawn line but the area of the coordinate plane that satisfies the inequality. This shows the boundary line for x + y < 6: (note that this does not show the inequality part) The difference is that the solution to the inequality is not the drawn line but the area of the coordinate plane that satisfies the inequality. Get the unbiased info you need to find the right school. Graph: y<2x-1 Find the x- and y-intercepts. SURVEY . In these cases, we use linear inequalities �inequalities that can be written in the form of a linear equation. The limits of an area can be determined by the boundary line. Closed half plane. One Variable Inequalities. In addition, since the original inequality is strictly greater than symbol, \Large{\color{red}>}, we will graph the boundary line as a dotted line. What's an Inequality? © copyright 2003-2020 Study.com. To learn more, visit our Earning Credit Page. You need to test whether the origin satisfies the inequality. Identify the shaded region, and the type of boundary line as dashed or solid, complete the inequality, check if the ordered pair is a solution, identify the inequalities, shade the region, graph the inequalities and much more. 1=2x Divide both sides by 2. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. Step 2. Step 3: Shade the region that satisfies the inequality . Learn vocabulary, terms, and more with flashcards, games, and other study tools. A boundary line, which is the related linear equation, serves as the boundary for the region.You can use a visual representation to figure out what values make the inequality true—and also which ones make it false. Step 3: Now graph the y = x + 1. }, Solution: P = sum of sides = 4 + 5 + 3 = 12 in. Working Scholars® Bringing Tuition-Free College to the Community. Type = for "less than or equal to". Graph solid boundary lines, as all the inequalities contain greater than or equal to signs. Identify the shaded region, and the type of boundary line as dashed or solid, complete the inequality, check if the ordered pair is a solution, identify the inequalities, shade the region, graph the inequalities and much more. Next, select a point that is not on the first boundary line, y ≤ −4x − 4, to determine which side of the line to shade. How do you do that? Tags: Question 12 . The boundary line for the inequality is drawn as a solid line if the points on the line itself do satisfy the inequality, as in the cases of $$\le$$ and $$\ge$$. Still, the solution points do not cross the boundary line and because the solution (inequality direction) is greater than, the shaded part is above the line. One side of the boundary line contains all solutions to the inequality Here you can see that one side is colored grey and the other side is colored white. In math, we use the term perimeter to indicate the distance around the outer edge of a shape. Shade in one side of the boundary line. To see that this is the case, choose a few test points 66 and substitute them into the inequality. OBJ: 1.2 Graph the boundary line between two half planes for each inequality in a system of linear inequalities, and justify the choice of solid or dashed lines. Defiance of an equation. A boundary line , which is the related linear equation, serves as the boundary for the region. 62/87,21 Sample answer: CHALLENGE Graph the following inequality. - Definition & Examples, Quiz & Worksheet - Boundary Lines in Math, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, Perpendicular Lines Lesson for Kids: Definition & Examples, Biological and Biomedical Notice, all the inequality symbols have an “equal to” component. Solutions to linear inequalities are a shaded half-plane, bounded by a solid line or a dashed line. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons When you are graphing inequalities, you will graph the ordinary linear functions just like we done before. Shade in the side of that boundary line where the inequality is true. Check to see if this point satisfies the inequality. plot the boundary line. To determine which side of the boundary line to shade, substitute a test point, such as (0, 0), into the original inequality, y > -4x -3. The boundary line is drawn as a dashed line (if This is a graph for a linear inequality. We could use any point as a test point, provided it is not on the line. just create an account. The inequality solver will then show you the steps to help you learn how to solve it on your own. Linear inequalities can be graphed on a coordinate plane.The solutions for a linear inequality are in a region of the coordinate plane. On one side lie all the solutions to the inequality. The boundary line is dashed for > and < and solid for ≥ and ≤. LESSON 1: Introduction to Inequalities: Working with ConstraintsLESSON 2: Emerging Pictures: Graphing Inequalities in Two VariablesLESSON 3: Two Methods, One Equation: Finding the Boundary LineLESSON 4: Writing and Graphing Inequalities to Represent ConstraintsLESSON 5: Finding the Feasible RegionLESSON 6: Where Do the Lines Cross? < or > There are four types of inequality signs: <, >, <=, >= If the boundary line is dashed then the inequality does not include that line. The graph of a linear inequality is always a half‐plane. We test the point 3;0 which is on the grey side. flashcard set{{course.flashcardSetCoun > 1 ? One side of the boundary line contains all solutions to the inequality. Introduction In this tutorial we will be looking at linear inequalities in two variables. If the original inequality is < or >, the boundary line is drawn as a dashed line, since the points on the line do not make the original sentence true. What Are Concurrent Lines? Graph the linear equation Ax + By = C. This line becomes a boundary line for the graph. New questions in Mathematics. This means that the solutions are NOT included on the boundary line. For an inequality in one variable, the endpoint is shown with a parenthesis or a bracket depending on whether or not is included in the solution: Graph the first inequality. What is the measure of the boundary line for this yard? Ax + By < C. Ax + By > C. Ax + By ≤ C. Ax + By ≥ C. To graph such sentences. Since the region below the line is shaded, the inequality should be ≤. Since the inequality contains an equals sign the boundary line will be a solid . Type = for "less than or equal to". So, the boundary line in an inequality shows the line past which solutions do not appear. Next, pick a point not on the line. When inequalities are graphed on a coordinate plane, the solutions are located in a region of the coordinate plane, which is represented as a shaded area on the plane. 6:36. Each of these mathematical concepts includes a boundary line. It is … On the same grid, graph the second inequality. x ≥ -1. x ≤ -1. x > -1. x < -1. what is the value of b in the equation 45 x -b HURRY UP IF YOU ANSWER THIS QUESTION CORRECT I WILL NAME YOU BRAINLY WHAT IS 129 SQUARED A farmer harvests crops on 2/5 acre of land in 1/3 hour. Solve x + 3 < 0.; If they'd given me "x + 3 = 0", I'd have known how to solve: I would have subtracted 3 from both sides.I can do the same thing here: Then the solution is: Again, the boundary line is y = x + 1, but this time, the line is solid meaning that the points on the line itself are included in the solution. The boundary line is vertical. credit-by-exam regardless of age or education level. what were the three outcomes of the battle of gettysburg, Lirik green day wake me up when september ends. The inequality is expressed in slope-intercept form in level 1 and has to be converted to slope-intercept form in Level 2. Boundary lines in math can relate to shapes or areas on an inequality graph. Use the method that you prefer when graphing a line. Similarly, all points below the boundary line, the side with (0, 0) (0, 0) and (−5, −15), (−5, −15), are not solutions to y > x + 4, y > x + 4, as shown in Figure 3.13. If the inequality is < or >, graph the equation as a dotted line.If the inequality is ≤ or ≥, graph the equation as a solid line.This line divides the xy - plane into two regions: a region that satisfies the inequality, and a region that does not. Ben's rectangular-shaped yard is 500ft across and 700ft deep. Yes, they are part of the solution set. You can test out of the We would like to show you a description here but the site won’t allow us. Identify and graph the boundary line. Udacity 137 views. No matter the shape of your property, the boundary line of your property will create a geometric shape. Use the method that you prefer when graphing a line. Many properties are rectangular, but not all are. This is because the mathematical sentence tells us that the solution is less than x + 1. Less Than Or Equal To. Graph the boundary line. answer choices .