[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-360003-105":59,"doc-detail-360003-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-a","Understanding Proportional Relationships—Review (A)","","Review worksheet focused on identifying proportional relationships and determining the constant of proportionality. It distinguishes proportional cases where y/x stays constant and the graph is a straight line through the origin from non-proportional situations where y/x varies or the line has a nonzero intercept. Tasks use tables, contextual word problems, and graphs, requiring students to compute k and write equations in the form y = kx.",{"@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-a/360003/",{"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-a/360003.png","ImageObject",300,407,{"name":92,"@type":93},"Riley West","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","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 relationship proportional?","Question",{"text":113,"@type":114},"A relationship is proportional when y/x equals the same constant k for all pairs, and the 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?",{"text":118,"@type":114},"Use k = y/x from the table values, or read k from the graph’s proportional pattern. Then write the equation as y = kx.",{"name":120,"@type":111,"acceptedAnswer":121},"How can you tell if a line is proportional from a graph?",{"text":122,"@type":114},"Check whether the line passes through the origin (0,0). If it passes through (0,0), it is proportional; if it crosses the y-axis at a nonzero value, it is not.","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},360003,1790377752,{"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},1099523885074,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Name:  \n______________________________________  \nUnderstanding Proportional Relationships—Review (A)  \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 | 5 | 10 | 15 | 20 |\n\nProportional?   Explain:  \n2.) Is this relationship proportional?  \n\n| x | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| y | 3 | 7 | 11 | 15 |\n\nProportional?   Explain:  \nPart 2—Constant of Proportionality (Tables)  \n3.) Context: hours worked, $ earned. Find k and write the equation y = kx.  \n| Hours Worked | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| Money Earned (in dollars) | 6 | 12 | 18 | 24 |\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: miles, gallons used. Find k and write the equation y = kx.  \n\n| Miles Driven | 4 | 8 | 12 | 16 |\n| --- | --- | --- | --- | --- |\n| Gas Used\u003Cbr>(in Gallons) | 3 | 6 | 9 | 12 |\n\nk =   Equation: y =  \n_______  \nPart 3—Proportional? (Graphs)  \n5.) A line passes through: (0, 0) (2, 6) (4, 12) (6, 18)  \nProportional?    \nExplain:  \n6.) A line passes through: (0, 3) (1, 6) (2, 9) (3, 12)  \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)  \n8.) Context: Total laps ran over time (in minutes)  \nk =   y = kx:    \nLaps in 12 minutes?    \n9.) Challenge Problem  \nA local bakery charges a fixed price per muffin.  \n| Number of\u003Cbr>Muffins Sold | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| Cost\u003Cbr>(in Dollars) | $3 | $6 | $9 | $12 |\n\na) Is this a proportional relationship? Find k and write the equation.  \nb) How much would 15 muffins cost?    \nc) How many muffins can you buy for $18?    \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 = 5 for all pairs  \n2.) No—y/x varies: 3/2, 7/4, 11/6, 15/8  \nPart 2—k from Tables:  \n3.) k = 6 y = 6x  \n4.) k = ~~3~~4 y = ~~3~~4x  \nPart 3—Proportional? (Graphs):  \n5.) Yes—straight line through origin  \n6.) No—straight line but y-intercept = 3, not 0  \nPart 4—k from Graphs:  \n7.) k = 52 Cost of 8 gallons? $20  \n8.) k = 2~~3~~ Laps in 12 minutes? 8 laps  \n9.) Challenge:  \na) Yes—proportional. k = 3/2 (= $1.50 per muffin) . Equation: y = 1.5x  \nb) 15 muffins: y = 1.5(15) = $22.50  \nc) $18 ÷ $1.50 = 12 muffins  \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)","cbCaipkXAzL4ImnD","https://ap.wps.com/l/cbCaipkXAzL4ImnD","pdf",1446938,"English","# Part 1—Proportional? (Tables)\n## 1.) Is this relationship proportional?\n## 2.) Is this relationship proportional?\n# Part 2—Constant of Proportionality (Tables)\n## 3.) Hours worked, money earned\n## 4.) Miles, gallons used\n# Part 3—Proportional? (Graphs)\n## 5.) Line through (0,0)\n## 6.) Line not through origin\n# Part 4—k from Graphs and Context\n## 7.) Constant from a graph\n## 8.) Laps over time\n## 9.) Challenge problem","[{\"question\":\"What makes a relationship proportional?\",\"answer\":\"A relationship is proportional when y/x equals the same constant k for all pairs, and the graph is a straight line through the origin (0,0).\"},{\"question\":\"How do you find the constant of proportionality, k?\",\"answer\":\"Use k = y/x from the table values, or read k from the graph’s proportional pattern. Then write the equation as y = kx.\"},{\"question\":\"How can you tell if a line is proportional from a graph?\",\"answer\":\"Check whether the line passes through the origin (0,0). If it passes through (0,0), it is proportional; if it crosses the y-axis at a nonzero value, it is not.\"}]","Understanding Proportional Relationships—Review (A) | PDF",1790138472]