[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-361406-105":59,"doc-detail-361406-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","understanding-proportional-relationshipsreview-part-b","Understanding Proportional Relationships—Review - Part B","","Review worksheet on proportional relationships and constant of proportionality. Guides students to determine whether table or graph data represents a proportional relationship using y/x = k and the requirement that the line passes through the origin, then to find k and write the equation y = kx. Includes table-based and graph-based problems, word contexts involving days/pages, ounces/cost, hours/earnings, and pushups/minutes, plus a challenge problem about constant speed and distance-time proportionality with equation finding and time calculation.",{"@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/understanding-proportional-relationshipsreview-part-b/361406/",{"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/understanding-proportional-relationshipsreview-part-b/361406.png","ImageObject",300,407,{"name":92,"@type":93},"Stanley","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-25","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",18,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What makes a proportional relationship proportional?","Question",{"text":113,"@type":114},"A proportional relationship has y/x = constant (k) for all pairs, and its graph is a straight line through the origin (0, 0).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you find the constant of proportionality k from a table?",{"text":118,"@type":114},"Compute k as y/x for the table values, then write the equation y = kx.",{"name":120,"@type":111,"acceptedAnswer":121},"How do you know from a graph whether a relationship is proportional?",{"text":122,"@type":114},"Check whether the graph is a straight line through the origin (0, 0). If it does not pass through the origin or is not linear, it is not proportional.","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},361406,1790386249,{"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,"preview_page_count":4},2336477405376,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Name:  \n______________________________________  \nUnderstanding Proportional Relationships—Review (B)  \nRemember: Proportional relationship: y/x = constant (k) for all pairs. The graph is a straight line through the origin (0, 0) . Constant of proportionality: k = y/x. Equation: y = kx. Non-proportional: y/x varies, or line does not pass through origin.  \nDirections: This review covers identifying proportional relationships and finding the constant of proportionality. Solve each problem. Show your work.  \nPart 1—Proportional? (Tables)  \n1.) Is this relationship proportional?  \n\n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 4 | 8 | 12 | 16 |\n\nProportional?   Explain:  \n2.) Is this relationship proportional?  \n\n| x | 1 | 3 | 5 | 7 |\n| --- | --- | --- | --- | --- |\n| y | 2 | 5 | 8 | 11 |\n\nProportional?   Explain:  \nPart 2—Constant of Proportionality (Tables)  \n3.) Context: days, pages read. Find k and write the equation y = kx.  \n\n| Number of\u003Cbr>Days | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Pages Read | 7 | 14 | 21 | 28 |\n\nk =   Equation: y =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n4.) Context: ounces, cost ($) . Find k and write the equation y = kx.  \n\n| Ounces of Water | 5 | 10 | 15 | 20 |\n| --- | --- | --- | --- | --- |\n| Cost to Purchase\u003Cbr>(in Dollars) | 3 | 6 | 9 | 12 |\n\nk =   Equation: y =  \n_______  \nPart 3—Proportional? (Graphs)  \n5.) A line passes through: (0, 0) (3, 5) (6, 10) (9, 15)  \nProportional?    \nExplain:  \n6.) A line passes through: (0, 0) (1, 2) (4, 8) (10 , 10)  \nProportional?    \nExplain:  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nPart 4—Constant of Proportionality (Graphs)  \n7.) Context: hours, $ earned.  \nk =   y = kx:    \nEarnings in 7 hours?    \n8.) Context: pushups, minutes.  \nk =   y = kx:    \nMinutes for 25 pushups?    \n9.) Challenge Problem  \nA car travels at a constant speed. After 2 hours it has gone 110 miles; after 4 hours, 220 miles; after 5 hours, 275 miles.  \na) Is this a proportional relationship? Find k and write the equation.  \nb) At this rate, how long will it take the car to travel 385 miles?  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nANSWER KEY  \nPart 1—Proportional? (Tables):  \n1.) Yes—y/x = 4 for all pairs  \n2.) No—y/x varies: 2, 5/3, 8/5, 11/7  \nPart 2—k from Tables:  \n3.) k = 7 y = 7x  \n4.) k = 35 y = 35x  \nPart 3—Proportional? (Graphs):  \n5.) Yes—straight line through origin  \n6.) No—passes through origin but curves—not linear  \nPart 4—k from Graphs:  \n7.) k = 4 Earnings in 7 hours? $28  \n8.) k = 25 Minutes for 25 pushups? 10 minutes  \nChallenge:  \na) Yes—proportional. k = 55 (miles per hour) . Equation: y = 55x  \nb) 385 ÷ 55 = 7 hours  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)","cbCaitz6o5GmiQ1m","https://ap.wps.com/l/cbCaitz6o5GmiQ1m","pdf",1159378,"English","# Part 1—Proportional? (Tables)\n## Is this relationship proportional?\n# Part 2—Constant of Proportionality (Tables)\n## Find k and write the equation y = kx\n# Part 3—Proportional? (Graphs)\n## Is this relationship proportional?\n# Part 4—Constant of Proportionality (Graphs)\n## Find k and solve for the requested value\n# Challenge Problem\n## Proportional relationship, find k, and determine travel time","[{\"question\":\"What makes a proportional relationship proportional?\",\"answer\":\"A proportional relationship has y/x = constant (k) for all pairs, and its graph is a straight line through the origin (0, 0).\"},{\"question\":\"How do you find the constant of proportionality k from a table?\",\"answer\":\"Compute k as y/x for the table values, then write the equation y = kx.\"},{\"question\":\"How do you know from a graph whether a relationship is proportional?\",\"answer\":\"Check whether the graph is a straight line through the origin (0, 0). If it does not pass through the origin or is not linear, it is not proportional.\"}]","Understanding Proportional Relationships—Review - Part B | PDF",1790144215]