[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-359296-105":59,"doc-detail-359296-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","interpreting-graphs-of-proportional-relationships-a","Interpreting Graphs of Proportional Relationships (A)","","Interpreting Graphs of Proportional Relationships (A) focuses on reading proportional relationship graphs to determine the unit rate k, write the equation, and interpret key points in context. Learners use the idea that a proportional graph is a straight line passing through (0,0), representing zero input equals zero output, and that the line follows y = kx. Problems guide interpreting given variables, computing values for specified x amounts, and applying the equation to answer real-world questions, including a challenge scenario.",{"@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/interpreting-graphs-of-proportional-relationships-a/359296/",{"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/interpreting-graphs-of-proportional-relationships-a/359296.png","ImageObject",300,407,{"name":92,"@type":93},"Jacob","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-28","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does (0,0) mean on a proportional relationship graph?","Question",{"text":113,"@type":114},"(0,0) means zero input gives zero output, such as 0 hours worked earning $0.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you find the unit rate k for a proportional relationship?",{"text":118,"@type":114},"For any point (x,y) on the line, k = y ÷ x. Use that k to write the equation y = kx.",{"name":120,"@type":111,"acceptedAnswer":121},"How do you use the equation to find y when x is given?",{"text":122,"@type":114},"Substitute the given x into y = kx. For example, if k = 7 and x = 8, then y = 7(8) = 56.","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},359296,1790219134,{"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},962084931830,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:  \n______________________________________  \nInterpreting Graphs of Proportional Relationships (A)  \nRemember: In a proportional relationship graph: the line is straight and passes through (0, 0) . The point (0, 0) means \"zero input = zero output.\" The point (1, k) shows the unit rate k—how much y changes per 1 unit of x. The equation is y = kx, where k = y ÷ x for any point on the line.  \nDirections: Use each graph to find k, write the equation, and interpret key points.  \nProblem 1  \n1.) A graph shows hours worked (x) and $ earned (y) .  \na) k = y ÷ x =    \nb) Equation: y =    \nc) What does (0, 0) mean?  \nd) How much is earned in 8 hours?  \nProblem 2  \n2.) A graph shows pounds of apples (x) and cost in dollars (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)  \nProblem 3  \n3.) A graph shows minutes swimming (x) and laps completed (y) .  \nProblem 4  \n4.) A graph shows cups of flour (x) and cups of water (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)  \nProblem 5  \n5.) A graph shows seconds (x) and heartbeats (y) .  \n6.) Challenge Problem  \nA graph of a dog’s walking data passes through (0,0) and (4, 6) .  \na) Find k and write the equation.  \nb) What does the point (4, 6) mean in context?  \nc) Use your equation to find how far the dog walks in 10 minutes.  \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  \n1.) k = 7 y = 7x  \nc) (0, 0) means 0 hours worked earns $0.  \nd) y = 7(8) = $56  \n2.) k = 2 y = 2x  \nc) (0, 0) means 0 pounds costs $0.  \nd) y = 2(9) = $18  \n3.) k = 12 y = 1/2 x  \nc) (0, 0) means 0 minutes = 0 laps.  \nd) y = 1/2(10) = 5 laps  \n4.) k = 23 y = 2/3 x  \nc) (0, 0) means 0 cups of flour needs 0 cups of water.  \nd) y = 2/3(12) = 8 cups  \n5.) k = 4 y = 4x  \nc) (0, 0) means 0 seconds = 0 heartbeats.  \nd) y = 4(15) = 60 heartbeats  \n6.) Challenge:  \na) k = 6 ÷ 4 = 3/2 . Equation: y = 3/2 x.  \nb) Point (4, 6): 4 minutes = 6 blocks walked.  \nc) y = 3/2(10) = 15 blocks  \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)","cbCaiaejRI3HA768","https://ap.wps.com/l/cbCaiaejRI3HA768","pdf",1189597,"English","# Problem 1\n## Hours worked and earned\n# Problem 2\n## Pounds of apples and cost\n# Problem 3\n## Minutes swimming and laps completed\n# Problem 4\n## Cups of flour and cups of water\n# Problem 5\n## Seconds and heartbeats\n# Challenge Problem\n## Dog walking data through (0,0) and (4,6)","[{\"question\":\"What does (0,0) mean on a proportional relationship graph?\",\"answer\":\"(0,0) means zero input gives zero output, such as 0 hours worked earning $0.\"},{\"question\":\"How do you find the unit rate k for a proportional relationship?\",\"answer\":\"For any point (x,y) on the line, k = y ÷ x. Use that k to write the equation y = kx.\"},{\"question\":\"How do you use the equation to find y when x is given?\",\"answer\":\"Substitute the given x into y = kx. For example, if k = 7 and x = 8, then y = 7(8) = 56.\"}]","Interpreting Graphs of Proportional Relationships (A) | PDF",1790136626]