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Additional word problems connect proportional relationships to real contexts such as earnings, gas mileage, running distance, rain collection, and texting cost rates, followed by an answer key for verification.",{"@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/constant-of-proportionalityfrom-tables-a-find-k-and-write-the-equation/358792/",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/constant-of-proportionalityfrom-tables-a-find-k-and-write-the-equation/358792.png","ImageObject",300,407,{"name":42,"@type":43},"Valentina","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-09-23",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the constant of proportionality k, and how is it calculated from a table?","Question",{"text":63,"@type":64},"k is calculated as k = y ÷ x. For each pair in the table, divide the y-value by the matching x-value to get the same k.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you write an equation for proportional relationships from k?",{"text":68,"@type":64},"After finding k, write y = kx. Substitute the appropriate values to solve for unknown x or y quantities.",{"name":70,"@type":61,"acceptedAnswer":71},"How is the challenge problem for texting cost handled?",{"text":72,"@type":64},"Use the rate as k = $0.05 per text, form the equation y = 0.05x, complete the ratio table, then compute how many texts fit the given total cost by dividing.","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},358792,1790218826,{"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":96,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145,"preview_page_count":4},13056703020460,"https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923","Name:  \n______________________________________  \nConstant of Proportionality—From Tables (A)  \nRemember: The constant of proportionality k = y ÷ x. Find k by dividing any y-value by its x-value—all pairs give the same k. Write the equation: y = kx. Use the equation to find unknown values by substituting and solving.  \nDirections: Find the constant of proportionality (k) for each table. Write y = kx.  \nPart 1—Find k and Write the Equation  \n1.) Hours worked and $ earned  \n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 7 | 14 | 21 | 28 |\n\nk =   Equation: y =    \n2.) Gallons of gas and miles driven  \n\n| x | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| y | 5 | 10 | 15 | 20 |\n\nk =   Equation: y =    \n3.) Lemons and cups of sugar  \n\n| x | 3 | 6 | 9 | 12 |\n| --- | --- | --- | --- | --- |\n| y | 1 | 2 | 3 | 4 |\n\nk =   Equation: y =    \n4.) Cups of flour and cups of water  \n\n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 3 | 6 | 9 | 12 |\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)  \n5.) Inches of rain and gallons collected  \n\n| x | 4 | 8 | 12 | 16 |\n| --- | --- | --- | --- | --- |\n| y | 3 | 6 | 9 | 12 |\n\nk =   Equation: y =    \n6.) Minutes and miles walked  \n\n| x | 5 | 10 | 15 | 20 |\n| --- | --- | --- | --- | --- |\n| y | 2 | 4 | 6 | 8 |\n\nk =   Equation: y =    \n7.) Pounds of apples and total cost ($)  \n\n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 4 | 8 | 12 | 16 |\n\nk =   Equation: y =    \n8.) Students and groups  \n\n| x | 6 | 12 | 18 | 24 |\n| --- | --- | --- | --- | --- |\n| y | 5 | 10 | 15 | 20 |\n\nk =   Equation: y =    \nPart 2—Find k and Complete the Table  \n9.) Hours and pages  \n\n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 3 |  | 9 |  |\n\nk =  \n_______  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \n10.) Gallons and cost ($)  \n\n| x | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| y |  | 10 |  | 20 |\n\nk =  \n_______  \n11.) km and miles  \n\n| x | 4 | 8 | 12 | 16 |\n| --- | --- | --- | --- | --- |\n| y | 3 |  |  | 12 |\n\nk =  \n_______  \n12.) Hours and earnings ($)  \n\n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 6 |  | 18 |  |\n\nk =  \n_______  \nPart 3—Word Problems  \n13.) A worker earns $9 per hour. x=hours, y=$ earned.  \n\n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 9 | 18 | 27 | 36 |\n\nk =   Equation: y =    \nHow much for 8 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)  \n14.) A car uses gas at a constant rate. x=gallons, y=miles.  \n\n| x | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| y | 3 | 6 | 9 | 12 |\n\nk =   Equation: y =    \nMiles on 10 gallons?    \n15.) x=minutes running, y=miles.  \n\n| x | 3 | 6 | 9 | 12 |\n| --- | --- | --- | --- | --- |\n| y | 2 | 4 | 6 | 8 |\n\nk =   Equation: y =    \nMiles in 18 minutes?    \n15.) Challenge Problem  \nA cell phone plan charges $0.05 per text message.  \na) Build a ratio table for 10, 20, 50, and 100 texts. Find k and write the equation.  \nb) How many texts can you send for $3 .75? Show your work.  \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 = 7 y = 7x 6.) k = 25 y = 25x  \n2.) k = 52 y = 52x 7.) k = 4 y = 4x  \n3.) k = 13 y = 13x 8.) k = 56 y = 56x  \n4.) k = 3 y = 3x  \n5.) k = 34 y = 34x  \nPart 2:  \n9.) k = 3 Missing: 6 | 12 11.) k = 34~~ ~~ Missing: 6 | 9  \n10.) k = 52~~ ~~ Missing: 5 | 15 12.) k = 6 Missing: 12 | 24  \nPart 3:  \n13.) k = 9 y=9(8)=$72  \n14.) k = 32~~ ~~ y=3/2(10)=15 miles  \n15.) k = 2  y=2/3(18)=12 miles 3  \n16.) Challenge: a) k = $0 .05/text. y = 0.","cbCaib1SXeyKOdUY","https://ap.wps.com/l/cbCaib1SXeyKOdUY","pdf",1975092,"English","# Part 1—Find k and Write the Equation\n## Equations for each table\n# Part 2—Find k and Complete the Table\n## Missing values using y = kx\n# Part 3—Word Problems\n## Proportional word problems and challenge\n# Answer Key","[{\"question\":\"What is the constant of proportionality k, and how is it calculated from a table?\",\"answer\":\"k is calculated as k = y ÷ x. For each pair in the table, divide the y-value by the matching x-value to get the same k.\"},{\"question\":\"How do you write an equation for proportional relationships from k?\",\"answer\":\"After finding k, write y = kx. Substitute the appropriate values to solve for unknown x or y quantities.\"},{\"question\":\"How is the challenge problem for texting cost handled?\",\"answer\":\"Use the rate as k = $0.05 per text, form the equation y = 0.05x, complete the ratio table, then compute how many texts fit the given total cost by dividing.\"}]","Constant of Proportionality—From Tables (A) - Find k and Write the Equation | PDF",1790135313,13]