[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267361-105":59,"doc-detail-267361-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","heart-of-algebra-linear-equations-coordinate-geometry-for-sat-math","Heart of Algebra - Linear Equations & Coordinate Geometry for SAT Math","","Heart of Algebra prepares students for SAT Math by teaching how to interpret, create, use, represent, and solve problems involving linear relationships. The material aligns with high school algebra expectations and emphasizes connections across multiple representations of linear functions. It covers the slope of a line, midpoint and distance concepts, equation forms, and relationships between parallel and perpendicular lines, supported by practice questions targeting SAT-style linear equation skills.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/heart-of-algebra-linear-equations-coordinate-geometry-for-sat-math/267361/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/heart-of-algebra-linear-equations-coordinate-geometry-for-sat-math/267361.png","ImageObject",300,407,{"name":92,"@type":93},"Jasmine","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",24,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics does Heart of Algebra cover for SAT Math?","Question",{"text":113,"@type":114},"It focuses on linear relationships, including linear equations and functions, systems of linear equations, linear inequalities, and absolute value.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the slope of a line determined in the material?",{"text":118,"@type":114},"The slope is found using two points on the line and expressed using a formula, then interpreted as the steepness and direction of the line.",{"name":120,"@type":111,"acceptedAnswer":121},"What relationships are used to identify parallel and perpendicular lines?",{"text":122,"@type":114},"Parallel non-vertical lines have equal slopes, while perpendicular non-vertical lines have slopes that are negative reciprocals of each other.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},267361,1790318769,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":52},2336478487870,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Heart of Algebra  \nFor Heart of Algebra questions on the SAT Math test , Students will interpret, create, use, represent, and solve problems using linear representations, and make connections between different representations of linear relationships, all from high school algebra courses preparatory for the math aligned with college and career readiness expectations. Knowledge Elements are as follows; Linear equations in one variable, Linear equations in two variables, Linear functions Systems of two linear equations in two variables, linear inequalities in one or two variables. There will be 13-15 questions on the SAT Math Test representing approximately a third of the Math Test.  \n\n|  |  | IvyBound Tutoring Services Ltd. /SATMath800 | 1 |  |  |\n| --- | --- | --- | --- | --- | --- |\n\nTABLE OF CONTENT  \nLinear Equation/ Coordinate Geometry…………………………………………………..…..3  \nLinear Function/ Linear Graph Translation…………………………………………………21  \nCreate Linear Expression in One Variable………………………………………….……….29  \nSolutions to Linear Equations……………………………………………….………………..35  \nSolving Linear Equations………………………………………………….………….……….41  \nLinear Equation in One Variable (Word Problems)…………………..……….……………47  \nLinear Equations in Two Variables...........................................................................................55  \nInterpreting Linear Functions…………………………………………………………………67  \nInterpreting Graphs of Linear Functions…………………………………………..…………77  \nSolution to System of Linear Equation……………………………………............…………..85  \nSolving System of Linear Equation……………………………………………….…..……….95  \nCreate and/or Solve System of Linear Equations……………………………………….…..104  \nGraphs of System of Linear Equations…………………………………………..……….….114  \nTransposition of Formulae……………………………………………………………………116  \nLinear Inequalities and Graph of Linear Inequalities………………………………………126  \nSystem of Linear Inequalities…………………………………………………………………145  \nAbsolute Value…………………………………………………………………………………157  \n.  \n\n|  |  | IvyBound Tutoring Services Ltd. /SATMath800 | 2 |  |  |\n| --- | --- | --- | --- | --- | --- |\n\nLinear Equations/Coordinate Geometry  \nThe slope ofa line  \nThe slope ofa line is a measure of the steepness of the line; large positive slope value means the line slope upwards and is steep.  \nTo find the slope ofa line, we need two points on the line.  \n1. From two points (􀝔1 , 􀝕1 ) and (􀝔2 , 􀝕2 ) Slope m = y~~ 2~~x2~~ ~~􀀐~~ ~~yx~~1~~1  \n2. From 􀝕 = 􀝉􀝔 + 􀜿  \n􀝉 = slope and 􀜿 = 􀝕 intercept.  \n3. The slope between any two points on aline is constant.  \nThe midpoint ofa line  \nGiven the two endpoints (􀝔1 , 􀝕1 ) and (􀝔2 , 􀝕2 ) the coordinates of the midpoint of the line segment are  \n􀝔1 + 􀝔2 􀝕1 + 􀝕2  \n2 , 2  \nDistance between two points.  \nThe distance between two points (􀝔1 , 􀝕1 ) and (􀝔2 , 􀝕2 ) is given by the formula  \n􀝀 =  \nEquation ofa line  \n􀁸 Slope form  \n􀝕 = 􀝉􀝔 + 􀜿  \n􀁸 General Form 􀜽􀝔 + 􀜾􀝕 = 􀜿  \n􀁸 Unit slope form 􀝔􀜽 + 􀝕􀜾 = 1  \nParallel Lines  \nTwo non-vertical lines are parallel if their slopes are equal and their y-intercept differs.  \nPerpendicular Lines  \nTwo non-vertical lines are perpendicular if one gradient is negative reciprocal of the other.  \n\n|  |  | IvyBound Tutoring Services Ltd. /SATMath800 | 3 |  |  |\n| --- | --- | --- | --- | --- | --- |\n\nPractice Questions: LINEAR EQUATIONS/COORDINATE GEOMETRY  \n1.   \nWhat is the slope of the line described by the equation?  \n1􀝔 + 12􀝔 = 5􀝕  \n 3   \nA)  \n10  \nB) 3  \n10 C) ~~ ~~  \n3  \nD) 4  \nA Line is defined by 6􀝔 − 5􀝕 = −4 what is the slope of the line?  \n3.   \nIn the 􀝔􀝕-plane, the graph of the linear function 􀝂 contains the points (0, 2) and (8, 34). Which equation defines 􀝂 , where  \n􀝕 = 􀝂 􀝔 ?  \n(A) 􀝂 􀝔 = 2􀝔 + 42  \n(B) 􀝂 􀝔 = 32􀝔 + 36  \n(C) 􀝂 􀝔 = 4􀝔 + 2  \n(D) 􀝂 􀝔 = 8􀝔 + 2  \n4.   \nThe graph of the linear function 􀝂 is shown, where 􀝕 = 􀝂 (􀝔) . which equation defines 􀝂?  \n(A) 􀝂 􀝔 = 0. 75􀝔 + 3  \n(B) 􀝂 􀝔 = 0. 75􀝔 − 3  \n(C) 􀝂 􀝔 = 1. 33􀝔 + 3  \n(D) 􀝂 􀝔 = 1. 33􀝔 − 3  \n5.  \nFor the Linear function 􀝂, the graph of  \n􀝕 = 􀝂 (􀝔) in the 􀝔􀝕-plane has a","cbCaidt6KjcPmi9t","https://ap.wps.com/l/cbCaidt6KjcPmi9t","pdf",1058705,"English","# Linear Equations/ Coordinate Geometry\n## The slope of a line\n## The midpoint of a line\n## Distance between two points\n## Equation of a line (slope form, general form)\n## Parallel Lines\n## Perpendicular Lines\n# Practice Questions: LINEAR EQUATIONS/COORDINATE GEOMETRY","[{\"question\":\"What topics does Heart of Algebra cover for SAT Math?\",\"answer\":\"It focuses on linear relationships, including linear equations and functions, systems of linear equations, linear inequalities, and absolute value.\"},{\"question\":\"How is the slope of a line determined in the material?\",\"answer\":\"The slope is found using two points on the line and expressed using a formula, then interpreted as the steepness and direction of the line.\"},{\"question\":\"What relationships are used to identify parallel and perpendicular lines?\",\"answer\":\"Parallel non-vertical lines have equal slopes, while perpendicular non-vertical lines have slopes that are negative reciprocals of each other.\"}]","Heart of Algebra - Linear Equations & Coordinate Geometry for SAT Math | PDF",1789417670]