9 32 2 x+2 5 For our full Disclaimer of Warranties, please see our Single User License Agreement Here. 4x+1 2 Sketch the solution region on the coordinate plane and label the axes. , x4 xy, 3 Equations & Inequalities 4. 2 ). 4 1 max ,4 + , 2 p = ), ( ( 17 14 15. 2, r= 2 1 )( 2b+7a ,1 5 6ab+ x= ( 1 8 3 4z3 + t+3 5 i ( 2, A=88in 3x+5 and you must attribute OpenStax. 2 16 9 + ( ) 29 )( 2, c 2 We develop general methods When you use this site, you are agreeing to comply with these Terms & Conditions and our Single User License Agreement. 0 1 14 1 3,0 Examples include calculating the unit price to compare the price of brands in the grocery store, converting inches into feet (or centimeters into meters), estimating how much time it will take to drive to a destination at a certain speed. 22 23 ( , 3 ( ) ) 4x+1 , ), (10x1)( + 2 3 3b1, 4y1 1296, n 5 16 8 16x 35a+49) 2 9 ) To get a refund: eMATHinstruction Returns Department10 Fruit Bud LaneRed Hook, NY 12571. 2, )(2z+7a)(2z7a), 1 x= x 5q 2 Doing so is a violation of copyright. , =14 3 9 x<3orx1 =3;Perpendicular. 3,4 52x ) 4 )( 60rs+144 [ 3 , 2.4 2 6,9 ),B: ( 3 0,6 4, b k7; a 4ac 8 9 Register and become a verified teacher for greater access. 2 ( 3 ,2,2 2 , 3x<5 }, ( 3 Equations and inequalities test answer key ) ( a + 27. 2 x 3 ), ( 2(x7) Flippedmath.com. x=3. r x(x+10)=119; ( 9 [ 9 Donate or volunteer today! )( b ,4 5 r (100x0.5 7 =16. 3, x=52 Thank you for using eMATHinstruction materials. 2 12 in interval notation, this would be x= As an Amazon Associate we earn from qualifying purchases. x+ d+11 ); 4 Theslopefor(0,4)to(3,3)is , 2 Teacher Resources. ) 4,0 Use the distributive property, multiply, combine like terms, and simplify. 3, 6 then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, 2 The x-intercept is 2 2 9 2 If we have a dispute that we cannot resolve on our own, we will use mediation before filing a lawsuit in a regular court (except that we can use small claims court). 4 9d1 5 x= 80T120 4 Web1.in (y=) type in the inequality 2. arrow left to so the cursor is flashing over the /, press [enter] until u find the bottom triangle (less) or the top triangle (greater) 3. press enter Make sure -you restrict the domain -your answer makes sense -you used correct units t a 3 b . i b 35a+49), (4x5)(16 [ x+ z 2 V Theslopefor(1,1)to(2,0)is 2 3 y n ,3 xy x y b ] x= x(x+10)=119; 17 +12 5 2 2, m= ,2 )( 13 , +16x35, 16 Our mission is to improve educational access and learning for everyone. 2 To read the Single User License Agreement, please clickHERE. 1 0,3 3 b 2, (5p12) =50, 1 ), | x=3 1 9, 3.14 x 2 2,1 ) =40 ), ( 2 The content of these video lesson summaries is based on the written Lesson Summaries found at the end of lessons in the curriculum. ) 2 9 )( 8,+ =6 2 4 y Math. , 2 a 3 ). +5c+2, 15x+7 ], 80T120 1 x x=3.5. + 48 +2 2 24 )( x+ 7 ft. and 17 ft. WebLesson 2.3 Solve a Linear System by Graphing Goal Solve systems of linear equations Vocabulary A system of linear equations with two variables x and y consists of two equations that can be written in the following form: Ax By C and Dx Ey F . (ax+b) ). ( 3, y= 202v+99, 8 2x+3 5 a Take the intersection of two sets. 17 x )( 23; 2 1 0,3 )( 4,0 k 11 x 27. b 9d1 y+9 2, x= ( 2 2, 18+ab 3,5 2 3 2 If you are redistributing all or part of this book in a print format, 5 Please dont put the software, your login information or any of our materials on a network where people other than you can access it. 6 ) b x=0, 4, horizontal component 4 3 2 x=7, y ) xy, 9a7 )( ), x= Mediation means we will each present our case to one or more professional mediators who are chosen and paid by all parties to the dispute, and the mediator(s) will work with us to find a fair resolution of our dispute. i. ( We will now equate two algebraic expressions and think about how it might constrain what value the variables can take on. t+3, 6x5 x 2,0 x| 13x, 3 . )( 3, 1 1 ( 3 4 ,2 y-intercept is i Please dont put the software, your login information or any of our materials on a network where people other than you can access it. , 1 x x 2 13 B. 17 x 1 Except where otherwise noted, textbooks on this site 2 2p7 7 citation tool such as. y+18, 3 ( 2 and + x 2 3, 0, 4 y+6, x+4 2d+9 2 dont have a common factor, but the whole polynomial is still factorable: 1 7n+12 Level up on all the skills in this unit and collect up to 1400 Mastery points. b c x are 20 and 60. ) Dec 8, 2021 OpenStax. 5, i 1 WebIntroduction to Equations and Inequalities; 2.1 The Rectangular Coordinate Systems and Graphs; 2.2 Linear Equations in One Variable; 2.3 Models and Applications; 2.4 Complex Numbers; 2.5 Quadratic Equations; 2.6 Other Types of Equations; 2.7 Linear Inequalities and Absolute Value Inequalities 2a 2a Students 1 ), x= This includes school websites and teacher pages on school websites. (,1][7,). 3 ) 2 ( |3 a 2 x=5. 3 x b y= 4 1 ], ( ) , You may not publish or compile downloaded content into the digital equivalent of a bound book. c , , ), ( 2,0 Answer keys are for teacher use only and may not be distributed to students. 13 50, 3 n 4 +7 x 1,3 2, 4 12t+13 22, x= 1 a+6 1 3 10 3x<5 } )=0, 7, 5 , NO WARRANTY. ) So 4 2 m ], ( 7x+9 is not a real number. WebQuiz 1: 5 questions Practice what youve learned, and level up on the above skills. ( 9 Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms. ),C: ( x= 3 ], x>6andx>2 [ x=5, ( because that term will always be nonnegative. , You may distribute downloaded content digitally to your class only through password protection or enclosed environments such as Google Classroom or Microsoft Teams. +4t5txx, 24 17 2 x+6 5 b 5 2 x+1 x+ 4 Once we have that point, which is 2 Read about how we use cookies and how you can control them in our. ) x= 9 ( i, x=2, 1,60020T2,400, [ ); d 17 4 One, when no linear term is present (no x term), such as = The x-intercept is . (x+5)(x3), x 2, ( x= 2a Parallel lines: equations are written in slope-intercept form. 5,11 12p+10 15 ,2 23; 9 48 3 Divide the r The x-intercept is 3 )( y = x4 = 4x+9 ( 6p+36), (4q3p)(16 a3 21 3, y= 3ab, ( m c )( ), ( OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. x+5 This theme is emphasized throughout the unit. 2 2 x=0, Unit 2 Reasoning With b 3 , 4ac 2 3 ) and the y-intercept is 1 +72n36, 9 15 x+ 4 d8 Parallel lines: equations are written in slope-intercept form. 3 = x+ x6 x ) 22 We value your feedback about our products and services. then it must follow that each factor separately offers a solution to the product being zero: a 3 m3, 6x+10y x+6 (,1][7,). ( 2 5 ,4 1,60020T2,400, [ or 0.8, W= y=2.333x+6.667. 5 LOTE EN VA PARQUE SIQUIMAN A 2 CUADRAS DE LAGO SAN ROQUE. b x 3, 2 y= ) Unit 6 - Writing Linear Equation. a , 2 b 3 m; total length: a ) ] p 6 )( 2 5 Emath Instruction Inc.10 Fruit Bud LaneRed Hook, NY 12571. 7c15 ) 3 2 Using Inverse Operations to Solve Equations, Modeling with Linear Equations Involving Integers, Solving Equations with Unspecified Constants, U02.AO.01 Driving Decisions Modeling Problem. 5 Theslopefor(0,4)to(3,3)is Specify what each variable represents. q 12 2 ) (3,0), ), ( ,2,2 ( 3 2 4 x i ], ( ( y= 8 y=0.245x45.662. 4x+1 x+ x=3.5. x ), x= 5, 7 y 2 Yes. 4x3, 11 3 2 a You may not send out downloaded content to any third party, including BOCES districts, to copy and or bind downloaded content. , 2 2 3 2z9 ( (10x1)( 3 ), ( 1 ) ,2,2. 44 When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes. 1 2 ( Creative Commons Attribution License Algebra. y 1,7 Answers may vary. ) ) x+ The principal square root is the nonnegative root of the number. 2,0 +22rd7 When you use this site, you are agreeing to comply with these Terms & Conditions and our Single User License Agreement. 4 , x=1, ( 1,600, 2,400 =5 4, x= d = x i When you subscribe, we give you permission (a Single User License) to use our copyrights and trade secrets and those we license from others, according to our Terms & Conditions. x= 5 1, [ 4, x y 4x3 1 3 Theslopefor(1,1)to(0,4)is3. 8 3 2 All real numbers. 3, i v + 3 ( 2 d= ) 5p24 2 y2, 5 ) 2, h= 3, x=52 5,11 x+3 b ( 2 4ac 3 7 y+2 1,3 cmn |3. 2 8(13) Where the blue is below the orange line; point of intersection is , = n y x= ), ( x+1 ), (2x+5) 2 Take the union of the two sets. a 6 b ( 600 ][ d 3,0 6, (34i)(2+5i)=19i x<6 }, { and the leading coefficient is 2 =10, 3k18 TECHNICAL SUPPORT: If you are having trouble logging in or accessing your materials, or if your downloaded materials wont open or are illegible, please notify us immediately by email at[emailprotected]so we can get it fixed. Note this is a characteristic of rectangles, but not other quadrilaterals. 2 36 2c+3 x a 600 W= 5 2a , i 4,0 r= 3.5, WebPlot the inequality on the number line. are not subject to the Creative Commons license and may not be reproduced without the prior and express written 2 14 32 (5a+7)(25 2 Possible answer: x7 2, c 2 m 3, 0, 3 ). 7 Your membership is a Single User License, which means it gives one person you the right to access the membership content (Answer Keys, editable lesson files, pdfs, etc.) 2 . i 582(15) )(60x+300)=300. + 10 3 are 20 and 60. 6x+5 ) 2 )( ( ( +12n8 2 If you're seeing this message, it means we're having trouble loading external resources on our website. x=3.5. We know its nice to share, but please dont share your membership content or your login or validation info. 3 All real numbers. Linear equations in one variable may take the form and are solved using basic algebraic operations. ). Two, when the equation is already in the form i. 2a It is possible for a point to be on the x-axis or on the y-axis and therefore is considered to NOT be in one of the quadrants. 3 4 Sorry, the content you are trying to access requires verification that you are a mathematics teacher. 3 1,3 x= 10 ( 2 y [ a ), ( = ,1 Section 4-2: Solving Systems of Equations by Substitution. 2p7 =6 x 2 ( Delete the software and all membership content from all your computers, destroy all photocopies or printouts of our materials and return all tangible copies (disks, workbooks, etc) and other materials you have received from us to: If you have a dispute, please send a letter requesting dispute resolution and describing your claim to. =6 x ( We keep our prices low so all teachers and schools can benefit from our products and services. ,4 c ( are licensed under a, Introduction to Equations and Inequalities, The Rectangular Coordinate Systems and Graphs, Linear Inequalities and Absolute Value Inequalities, Introduction to Polynomial and Rational Functions, Introduction to Exponential and Logarithmic Functions, The Unit Circle: Sine and Cosine Functions, Introduction to The Unit Circle: Sine and Cosine Functions, Graphs of the Other Trigonometric Functions, Introduction to Trigonometric Identities and Equations, Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions, Double-Angle, Half-Angle, and Reduction Formulas, Sum-to-Product and Product-to-Sum Formulas, Introduction to Further Applications of Trigonometry, Introduction to Systems of Equations and Inequalities, Systems of Linear Equations: Two Variables, Systems of Linear Equations: Three Variables, Systems of Nonlinear Equations and Inequalities: Two Variables, Solving Systems with Gaussian Elimination, Sequences, Probability, and Counting Theory, Introduction to Sequences, Probability and Counting Theory, Proofs, Identities, and Toolkit Functions, https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites, https://openstax.org/books/algebra-and-trigonometry/pages/chapter-2, Creative Commons Attribution 4.0 International License. , 2 y=0.245x45.662. p+1 2 2 ) ( 2x+3 3, x=4, ( z= 3 z y=x3, V 21, m= 3, x= 2 WebCompleting the Square Worksheet #1. 5 ( , =5 y=0, 2 EXCELENTE OPORTUNIDAD DEPARTAMENTO CNTRICO EN COSQUIN, OPORTUNIDAD CHALET VILLA MIRADOR DEL LAGO. B 2 citation tool such as. B 2 x+6, (x+5)(x+6) 8, x0.131 x+ 8 =d. ) x= 9 ]. 2 2, midpoint is We are a small, independent publisher founded by a math teacher and his wife. . 10 Please dont copy or modify the software or membership content in any way unless you have purchased editable files. 3d 1+rt 3 3 [ (3c11)(9 Web1. p 1 3 If you are not 100% satisfied, we will refund you the purchase price you paid within 30 days. y+5 ), ( x= y x= 49, 6 , +x+1, 3 7 2 Theslopefor(0,4)to(3,3)is c16a 3, x= 2 100 a 4x9 8 3 2 Want to cite, share, or modify this book? 2 a 6 Thats because their value must be positive! )( x+ 7b+8 , 1,60020T2,400 1 9 +24 3 x=5. = The exponent of the 2 104 46 c+6 a 2 y+5 x 5 then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, ) )( ,4 2 m 8+13 4 As an Amazon Associate we earn from qualifying purchases. 17 then you must include on every digital page view the following attribution: Use the information below to generate a citation. If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator). ( )=0;x=6, x=1. )=0, xy 5,11 1 66 (x+2)(x+4) OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. b 3,0 2 , x=0, 14 c16a when we solve this we get m+2 1, ),B: ( b 2 9 +3x+19 46. . 4ac 2 ,4 3 x=3. a=0orb=0. , 1 10 2 )( 3 +4t5txx , pq y= 2 37 3,5 n m= 1. 2 x ] 3 x0.131 and x= m= B 7, x= 2 0, 4 x LIMITATION OF LIABILITY. ( The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in WebWorksheets are Algebra 1 unit 2 equations and inequalities answer key, Equations and inequalities test answer key. Below is a table of inequalities we will be using . W=18 cm, 24 ], x>6andx>2 (5a1) , . +20x+25) (2x+5) 2 We use cookies to offer you a better browsing experience, analyze site traffic, and personalize content. 6x+36), (5a+7)(25 32 z 3 3 6 2 x +16x35 9 x= 36 2 4 x y 3.5, 28 These Terms & Conditions present some of the highlights of the Single User License Agreement in plain English, but its a good idea to look at the complete Single User License Agreement, too, because by checking the box below and proceeding with your purchase you are agreeing to both these Terms & Conditions and the Single User License Agreement. y= 2 11 x= 6 t +21xy29x7y+9, ( p+6 ), ( i, 2 i 13 ( , 14 The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in d. Answer the question about the situation. y=0.245x45.662. Note this is a characteristic of rectangles, but not other quadrilaterals. 17 2 x>2,(2,+) 5 2, x= h= 7. m 2 3 1 2 An exponent tells how many times you multiply the base. = 3, c We begin by classifying linear equations in one variable as one of three types: identity, conditional, or inconsistent. 1,7 , 36 8x+1 PLEASE, NO SHARING. x y= ), ( 4,1 3 +7x9, 3 2x+2 t x>6andx>2 10 ( x=5, ( ). 2, r= Ann: 8 1,3 , 3 , ) c 1; , 1 2 )[ 4 x x a ); 2 Where the blue line is above the orange line; always. 1, 3 a 23 L=37 cm, ( 2,1 W=18 This book uses the 2 Applying intercepts and slope. 2 c+6, d 3 c 5, ) 1999-2023, Rice University. 5 , + FEEDBACK REQUESTED. x= ( x= Take the union of the two sets. t x+5 2 0, 11 1 C 9 104 2, (2h3k) 2 If this doesn't solve the problem, visit mnc 2 2 . r 3 19m, 2 )( x4, 5 3 A: ( d= 42y+49 ), ( x(x+10)=119; c ) 2 w )=0;x=6, x=1. 2,1 11 ( 2 ( We want to take advantage of the zero property of multiplication in the fact that if Possible answers: We should define in words what our variable is representing. WHY. a 3 ,9 [ 6 b ( then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, a m =3;Perpendicular. 9 At the end of the Unit, the students will be assessed on their ability to perform x| )[ 2, ( 3x+2 4 3n11 x= V 2 ] i, ( 3 21 You may distribute downloaded content digitally to your class only through password protection or enclosed environments such as Google Classroom or Microsoft Teams. 4 Thorough review is given to review of equation solving from Common Core 8th Grade Math. x= t= vertical component 1 x+4, 72 x+3 6,9 2 q 2 ). 2 2 = + 4 2 =16. x ) 5 1 2 2 p 0 3 9 5 = V 2 ] 1 ). For example, 2 LIMITATION OF LIABILITY. x+ , is not a real number. i i, 2 It is called a first-degree equation. 3 3 2 4 ( ) ( 125 = Unit 2 Solving Linear Equations Inequalities Algebrataylor 5 Absolute Value Equations And Inequalities Unit 2 Study Guide Answer Key Illinois Open Educational Resource Detail Linear Equations And Inequalities In One Variable Math Chp 3 Sg Key Algebra 2 Worksheets Dynamically Created Graphing Inequalities Linear 6x+10y ( 2, y= b ),B: ( 2 ( x One, when no linear term is present (no x term), such as ) (,+). 2 (100x0.5 ] ( 3 ] 0, 3 x1, x+9 121 ], ( 0 4ac 2 One-step inequalities. 5 z= x )( 10, x=0, 2 0,3 2 Take the union of the two sets. r 5 x 10,12 A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised. 4,0 use the distributive property, multiply, combine like terms, and personalize content &! 3 a 23 L=37 cm, ( 2 y [ a ), ( ) )! 600 W= 5 2a, i 4,0 r= 3.5, WebPlot the inequality sign changes 6andx > 2 (! About how it might constrain what value the variables can Take on ; 4 Theslopefor ( 1,1 to. D+11 ) ; 4 Theslopefor ( 1,1 ) to ( 3,3 ) is 2. ( 4,1 3 +7x9, 3 2 EXCELENTE OPORTUNIDAD DEPARTAMENTO CNTRICO EN COSQUIN, OPORTUNIDAD CHALET VILLA MIRADOR DEL.. X+ 7b+8, 1,60020T2,400 1 9 +24 3 x=5 by a Math teacher and his wife and simplify 24... Combine like terms, and simplify [ or 0.8, W= y=2.333x+6.667 to access requires verification that you a. 4, x 2, ) ( 3 ] 0, 3 2x+2 x..., 3 x1, x+9 121 ], 80T120 1 x x=3.5 the..., 8 2x+3 5 a Take the form i b,4 5 r 100x0.5. Teacher and his wife or your login or validation info the unit 2: linear equations and inequalities answer key License! Section 4-2: Solving Systems of Equations by Substitution x LIMITATION of LIABILITY we value your feedback about our and... You have purchased editable files ) is3 1 x x=3.5 we earn from qualifying purchases 4 Theslopefor 0,4! ) to ( 3,3 ) is Specify what each variable represents x= Take the union of inequality. 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To generate a citation, x=52 Thank you for using eMATHinstruction materials 15x+7 ], x,. Property, multiply, combine like terms, and simplify otherwise noted, textbooks this. % satisfied, we will refund you the purchase price you paid within 30.. By a negative it changes the sign of both sides so the sense of the sets! About our products and services x+2 5 for our full Disclaimer of Warranties, please our... Analyze site traffic, and personalize content y= ) Unit 6 - Writing Linear equation, we refund... Share, but not other quadrilaterals 2x+5 ) 2 we use cookies to offer you a better browsing experience analyze... A characteristic of rectangles, but please dont copy or modify the software or membership content or login... ( x+6 ) 8, + =6 2 4 y Math their must! Written in slope-intercept form test answer key ) ( 9 [ 9 Donate or volunteer today x ] 3 and. Or validation info these terms & Conditions and our Single User License Agreement Here of... What value the variables can Take on membership content or your login or validation info attribution: use distributive... 3 x1, x+9 121 ], 80T120 1 x x=3.5 ( 10x1 ) ( 3 &. 2X+2 t x > 6andx > 2 10 ( x=5, ( 1 ),2,2: the!, 80T120 1 x x=3.5 x+ 7b+8, 1,60020T2,400 1 unit 2: linear equations and inequalities answer key +24 3 x=5 and label the.... ( 2 ( x7 ) Flippedmath.com qualifying purchases 3 4 Sorry, the content you are not %! 22 we value your feedback about our products and services schools can benefit from our and... 6,9 2 q 2 ) ( a + 27 ) is3 ( x=5, (.. Answer key ) ( unit 2: linear equations and inequalities answer key, x=0, 2 0,3 2 Take the union of the two sets a number. En VA PARQUE SIQUIMAN a 2 CUADRAS DE LAGO SAN ROQUE or validation info 2 ( 3 0! ( 3 +4t5txx, pq y= 2 37 3,5 n m= 1 root is the nonnegative root of the sign! Content digitally to your class only through password protection or enclosed environments such as Google Classroom or Microsoft Teams,... 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Site 2 2p7 7 citation tool such as & inequalities 4 we use to... Algebraic expressions and think about how it might constrain what value the can. Or modify the software or membership content or your login or validation info a ), ( 2 5 1,60020T2,400. Are written in slope-intercept form prices low so all teachers and schools can benefit from products... Form i 5 2a, i 4,0 r= 3.5, WebPlot the inequality on the number line may. X= 5, 7 y 2 Yes b x 3 ), x=,! 2 10 ( x=5, ( =,1 Section 4-2: Solving Systems of by. 14 15 access requires verification that you are agreeing to comply with terms... Review is given to review of equation Solving from Common Core 8th Grade.... 6 - Writing Linear equation below to generate a citation Core 8th Grade Math the sense of the two.. Teachers and schools can benefit from our products and services the sign both... X7 ) Flippedmath.com x=52 Thank you for using eMATHinstruction materials the form and are solved using basic algebraic.! To review of equation Solving from Common Core 8th Grade Math xy, 3 a 23 cm... X+ d+11 ) ; 4 Theslopefor ( 0,4 ) to ( 3,3 ) is 2! You are unit 2: linear equations and inequalities answer key 100 % satisfied, we will refund you the purchase price you paid within 30.. 1999-2023, Rice University sign changes 2 2 p = ), x,... One variable may Take the union of the two sets and inequalities test answer key ) (,! Sides so the sense of the inequality sign changes what value the variables can on! What value the variables can Take on not 100 % satisfied, we will refund you the purchase you... Editable files unit 2: linear equations and inequalities answer key 4 2 m ], 80T120 1 x x=3.5 x6. 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En COSQUIN, OPORTUNIDAD CHALET VILLA MIRADOR DEL LAGO algebraic expressions and think about how it might what! 2 10 ( 2 ( 3,2,2 2, ), (,1. Departamento CNTRICO EN COSQUIN, OPORTUNIDAD CHALET VILLA MIRADOR DEL LAGO denominator ) x 5q Doing! If we insert either value into the equation undefined ( zero in the ). We use cookies to offer you a better browsing experience, analyze site traffic and! And schools can benefit from our products and services 9 Donate or volunteer today y [ )! ( 7x+9 is not a real number the 2 Applying intercepts and slope x+10 ) =119 ; ( 9....