[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-360389-105":59,"doc-detail-360389-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","constant-of-proportionalityfrom-graphs-b-work-sheets","Constant of Proportionality—From Graphs (B) - Work Sheets","","Constant of Proportionality—From Graphs (B) trains learners to determine the proportionality constant k from graph points and write the corresponding equation y = kx. The worksheet is organized into three parts: finding k for multiple real-world contexts (hours and earnings, cups of flour and water, km and miles, liters and grams, seconds and heartbeats, ounces and cost), applying the equation to predict values, and solving real-world graph problems including heart rate data, bulk-food cost, and a Mars rover distance challenge. An answer key is included.",{"@graph":69,"@context":122},[70,84,105],{"@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/constant-of-proportionalityfrom-graphs-b-work-sheets/360389/",{"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/constant-of-proportionalityfrom-graphs-b-work-sheets/360389.png","ImageObject",300,407,{"name":92,"@type":93},"Fahsai","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-24","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the constant of proportionality k from a graph?","Question",{"text":112,"@type":113},"Pick a non-origin point (x, y) on the line and compute k = y ÷ x. Then use y = kx for the proportional relationship.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does the equation y = kx represent in these problems?",{"text":117,"@type":113},"It links the variables x and y through the proportionality constant k, so multiplying x by k gives y.",{"name":119,"@type":110,"acceptedAnswer":120},"How is k used to answer questions like “Earnings in 9 hours” or “Miles in 20 km”?",{"text":121,"@type":113},"First determine k from the given points, write the equation y = kx, then substitute the requested x value to compute y.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},360389,1790513597,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","Name:  \n______________________________________  \nConstant of Proportionality—From Graphs (B)  \nRemember: From a graph: pick any point (x, y) on the line (not the origin) . Compute k = y ÷ x. The constant of proportionality is the slope of the line through the origin. Write the equation: y = kx.  \nDirections: Use the given points to find the constant of proportionality (k) . Then write the equation y =  \nkx.  \nPart 1—Find k from the Graph  \n1.) Context: hours and earnings ($) .  \nk =  \n_______  \nEquation: y =    \n2.) Context: cups flour and cups water.  \nk =  \n_______  \nEquation: y =    \n3.) Context: km and miles.  \nk =  \n_______  \nEquation: y =    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n4.) Context: liters and grams.  \nk =  \n_______  \nEquation: y =    \n5.) Context: seconds and heartbeats.  \nk =  \n_______  \nEquation: y =    \n6.) Context: ounces and cost ($) .  \nk =  \n_______  \nEquation: 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)  \nPart 2—Find k and Use the Equation  \n7.) Context: hours, earnings ($) . Points: (1, 4) (2, 8) (3, 12)  \nk =  \n_______  \ny = kx:    \nEarnings in 9 hours?    \n8.) Context: cups flour, cups water. Points: (3, 5) (6, 10) (9, 15)  \nk =  \n_______  \ny = kx:    \nWater for 12 cups flour?    \n9.) Context: km, miles. Points: (4, 3) (8, 6) (12, 9)  \nk =  \n_______  \ny = kx:    \nMiles in 20 km?    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nPart 3—Real-World Graph Problems  \n10.) A heart rate monitor: x = seconds, y = heartbeats.  \nGraph passes through given points. Points: (1, 6) (2, 12) (4, 24)  \nk = _______ y = _______  \nHeartbeats in 8 seconds? _______________  \n11.) x = ounces, y = cost ($) . A bulk-foods scale records these data points. Points: (5, 3) (10, 6) (15, 9)  \nk = _______ y = _______  \nCost of 25 ounces? _______________  \n12.) Challenge Problem  \nA Mars rover’s distance from its launch site is plotted.  \nPoints: (3 hours, 1.2 km), (6 hours, 2.4 km), (10 hours, 4 km) .  \na) Find k and write the equation y = kx. What does k represent?  \nb) Use your equation to find how far the rover travels in 24 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)  \nANSWER KEY  \nPart 1:  \n1.) k = 4 y = 4x 4.) k = 92 y = 92x  \n2.) k = 53 y = 53x 5.) k = 6 y = 6x  \n3.) k = 34 y = 34x 6.) k = 35 y = 35x  \nPart 2:  \n7.) k = 4 k=4. y=4(9)=$36  \n8.) k = 5 k=5/3 . y=5/3(12)=20 cups 3  \n3  \n9.) k = k=3/4. y=3/4(20)=15 miles  \n4  \nPart 3:  \n10.) k = 6 k=6. y=6(8)=48 heartbeats  \n11.) k = 35~~ ~~ k=3/5. y=3/5(25)=$15  \n12.) Challenge: a) k = 1.2/3 = 0.4 km per hour. k is the rover’s speed. b) y = 0.4(24) = 9.6 km  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)","cbCaijkBuoMIlB0w","https://ap.wps.com/l/cbCaijkBuoMIlB0w","pdf",1319677,"English","# Part 1—Find k from the Graph\n## 1) Context: hours and earnings ($)\n## 2) Context: cups flour and cups water\n## 3) Context: km and miles\n## 4) Context: liters and grams\n## 5) Context: seconds and heartbeats\n## 6) Context: ounces and cost ($)\n# Part 2—Find k and Use the Equation\n## 7) Hours, earnings ($) with given points\n## 8) Cups flour and cups water with given points\n## 9) km, miles with given points\n# Part 3—Real-World Graph Problems\n## 10) Heart rate monitor\n## 11) Bulk-foods cost\n## 12) Challenge Problem (Mars rover)","[{\"question\":\"How do you find the constant of proportionality k from a graph?\",\"answer\":\"Pick a non-origin point (x, y) on the line and compute k = y ÷ x. Then use y = kx for the proportional relationship.\"},{\"question\":\"What does the equation y = kx represent in these problems?\",\"answer\":\"It links the variables x and y through the proportionality constant k, so multiplying x by k gives y.\"},{\"question\":\"How is k used to answer questions like “Earnings in 9 hours” or “Miles in 20 km”?\",\"answer\":\"First determine k from the given points, write the equation y = kx, then substitute the requested x value to compute y.\"}]","Constant of Proportionality—From Graphs (B) - Work Sheets | PDF",1790139896,13]