[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-267344-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-267344-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","easy-linear-func-eq-ineq-key","EASY linear func - eq - & ineq KEY","","Practice assessment items for SAT Math covering algebra skills in linear functions, linear equations (one and two variables), and linear inequalities (one or two variables). Each problem provides a question prompt, multiple-choice options, a designated correct answer, and a step-by-step rationale explaining how the equation or inequality structure leads to the selected choice. Difficulty is labeled as easy, with content focused on interpreting mathematical models and applying algebraic operations.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/easy-linear-func-eq-ineq-key/267344/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/easy-linear-func-eq-ineq-key/267344.png","ImageObject",300,407,{"name":42,"@type":43},"Cart","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-22","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",14,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How is the correct choice determined in the linear function total cost problem?","Question",{"text":63,"@type":64},"The rationale sets the monthly payment value into the given total-cost linear equation. Substituting the payment into the model yields the total cost, matching the selected option.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"In the yogurt pricing problem, what does each term represent?",{"text":68,"@type":64},"The explanation links variables to container counts and shows that the coefficient multiplied by the number of smaller containers gives the total sales from smaller containers. That value implies the per-container price for smaller containers.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you find the slope of a line perpendicular to another line?",{"text":72,"@type":64},"The rationale uses the opposite reciprocal relationship for perpendicular slopes. After identifying the original slope, it applies the opposite reciprocal to get the perpendicular line’s slope.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},267344,1789417379,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145},18829141979164,"https://eur-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Question ID 88e13c8c  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Algebra | Skill\u003Cbr>Linear functions | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 88e13c8c  \nThe total cost  , in dollars, to lease a car for  months from a particular car dealership is given by  \n, where  is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is ?  \nA.   \nB.   \nC.   \nD.   \nID: 88e13c8c Answer  \nCorrect Answer: C  \nRationale  \nChoice C is correct. It's given that 􀝂􀝔 is the total cost, in dollars, to lease a car from this dealership with a monthly payment of 􀝔 dollars. Therefore, the total cost, in dollars, to lease the car when the monthly payment is $ 400 is represented by the value of 􀝂􀝔 when 􀝔 = 400. Substituting 400 for 􀝔 in the equation 􀝂􀝔 = 36􀝔 + 1,000 yields 􀝂400 = 36400 + 1,000, or  \n􀝂400 = 15,400 . Thus, when the monthly payment is $ 400, the total cost to lease a car is $ 15,400 . Choice A is incorrect and may result from conceptual or calculation errors.  \nChoice B is incorrect and may result from conceptual or calculation errors.  \nChoice D is incorrect and may result from conceptual or calculation errors.  \nQuestion Difficulty: Easy  \nQuestion ID ee846db7  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Algebra | Skill\u003Cbr>Linear equations in two variables | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: ee846db7  \nA store sells two different-sized containers of a certain Greek yogurt. The store’s sales of this Greek yogurt totaled  dollars last month. The equation  represents this situation, where  is the number of smaller containers sold and  is the number of larger containers sold. According to the equation, which of the following represents the price, in dollars, of each smaller container?  \nA.     \nB.   \nC.     \nD.     \nID: ee846db7 Answer  \nCorrect Answer: A  \nRationale  \nChoice A is correct. It's given that the store's sales of a certain Greek yogurt totaled 1,277 .94 dollars last month. It's also given that the equation 5.48􀝔 + 7.30􀝕 = 1,277 .94 represents this situation, where 􀝔 is the number of smaller containers sold and 􀝕 is the number of larger containers sold. Since 􀝔 represents the number of smaller containers of yogurt sold, the expression 5.48􀝔 represents the total sales, in dollars, from smaller containers of yogurt. This means that 􀝔 smaller containers of yogurt were sold at a price of 5.48 dollars each. Therefore, according to the equation, 5.48 represents the price, in dollars, of each smaller container.  \nChoice B is incorrect. This expression represents the total sales, in dollars, from selling 􀝕 larger containers of yogurt. Choice C is incorrect. This value represents the price, in dollars, of each larger container of yogurt.  \nChoice D is incorrect. This expression represents the total sales, in dollars, from selling 􀝔 smaller containers of yogurt. Question Difficulty: Easy  \nQuestion ID 5b8a8475  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Algebra | Skill\u003Cbr>Linear equations in two variables | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 5b8a8475  \nLine  is defined by  . Line  is perpendicular to line  in the xy-plane. What is the slope of line ? A.  ~~ ~~~~ ~~  \nB.  ~~ ~~~~ ~~  \nC.  ~~ ~~  \nD.  ~~ ~~~~ ~~  \nID: 5b8a8475 Answer  \nCorrect Answer: A  \nRationale  \nChoice A is correct. It's given that line 􀝆 is perpendicular to line 􀝇 in the xy-plane. It follows that the slope of line 􀝆 is the opposite reciprocal of the slope of line 􀝇 . The equation for line 􀝇 is written in slope-intercept form 􀝕 = 􀝉􀝔 + 􀜾, where 􀝉 is the slope of the line and 􀜾 is the y-coordinate of the y-intercept of the line. It follows that the slope of line 􀝇 is 3. The opposite reciprocal of a number is-1 divided by the number. Thus, the opposite reciprocal of 3 is- ~~ ~~13. Therefore, the slope of line 􀝆 is-13.  \nChoice B is incorrect and may result from conceptual or calculation errors.  \nChoice C is incorrect and may result from conceptual or calculation errors.  \nChoice","cbCaipRrl0uSZXRs","https://ap.wps.com/l/cbCaipRrl0uSZXRs","pdf",5103293,143,"English","# Linear functions\n## Linear functions problems\n# Linear equations in two variables\n## Two-variable equation problems\n# Linear equations in one variable\n## One-variable equation problem\n# Linear inequalities in one or two variables\n## Inequality system problem","[{\"question\":\"How is the correct choice determined in the linear function total cost problem?\",\"answer\":\"The rationale sets the monthly payment value into the given total-cost linear equation. Substituting the payment into the model yields the total cost, matching the selected option.\"},{\"question\":\"In the yogurt pricing problem, what does each term represent?\",\"answer\":\"The explanation links variables to container counts and shows that the coefficient multiplied by the number of smaller containers gives the total sales from smaller containers. That value implies the per-container price for smaller containers.\"},{\"question\":\"How do you find the slope of a line perpendicular to another line?\",\"answer\":\"The rationale uses the opposite reciprocal relationship for perpendicular slopes. After identifying the original slope, it applies the opposite reciprocal to get the perpendicular line’s slope.\"}]","EASY linear func - eq - & ineq KEY | PDF",360]