[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-360079-105":59,"doc-detail-360079-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","writing-equations-for-proportional-relationships-a","Writing Equations for Proportional Relationships (A)","","Worksheet for learning proportional relationships by writing linear equations in the form y = kx. Students find the constant of proportionality k from tables by dividing y by x, then form equations and use them to compute missing values in multi-step practice items. It also includes problems that require translating descriptions and word statements into equations, solving for hours, pages, gallons, costs, minutes, and additional challenge work using constant rates.",{"@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/writing-equations-for-proportional-relationships-a/360079/",{"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/writing-equations-for-proportional-relationships-a/360079.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",21,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find the constant of proportionality k in y = kx?","Question",{"text":113,"@type":114},"When y is proportional to x, divide any y-value by its corresponding x-value: k = y ÷ x. Then use k to write the equation y = kx.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What steps should you follow to solve for a missing value using y = kx?",{"text":118,"@type":114},"Write the equation y = kx using the given k (from a table or description). Substitute the known x or y value, then solve for the unknown variable.",{"name":120,"@type":111,"acceptedAnswer":121},"What do the word problems ask you to do?",{"text":122,"@type":114},"Translate real situations with constant rates into an equation y = kx, then answer questions such as cost for a number of hours, gallons for a distance, or sugar for a given number of cookies.","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},360079,1790215626,{"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":81,"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":39,"preview_page_count":8,"preview_urls":145},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Name:  \n______________________________________  \nWriting Equations for Proportional Relationships (A)  \nRemember: If y is proportional to x, the relationship can be written as y = kx, where k is the constant of proportionality. Find k by dividing any y-value by its x-value: k = y ÷ x. Then substitute known values to solve for unknowns.  \nDirections: Find k, write the equation y = kx, and use it to solve problems.  \nPart 1—Find k from the Table, Write the Equation  \n1.) hours worked / $ earned  \n| x | 1 | 2 | 3 | 4 |\n| --- | --- | --- | --- | --- |\n| y | 5 | 10 | 15 | 20 |\n\nk = y ÷ x =   Equation: y =   x  \n2.) gallons / miles driven  \n\n| x | 2 | 4 | 6 | 8 |\n| --- | --- | --- | --- | --- |\n| y | 3 | 6 | 9 | 12 |\n\nk = y ÷ x =   Equation: y =   x  \n3.) cups flour / cups sugar  \n\n| x | 3 | 6 | 9 | 12 |\n| --- | --- | --- | --- | --- |\n| y | 1 | 2 | 3 | 4 |\n\nk = y ÷ x =   Equation: y =   x  \n4.) inches / centimeters  \n| x | 4 | 8 | 12 | 16 |\n| --- | --- | --- | --- | --- |\n| y | 3 | 6 | 9 | 12 |\n\nk = y ÷ x =   Equation: y =   x  \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—Write the Equation from the Description  \n5.) A car travels 60 miles per hour.  \nEquation:    \n6.) Apples cost $1.25 per pound.  \nEquation:    \nPart 3—Use the Equation to Find the Missing Value  \n9.) Equation: y = 4x hours / pages read If x = 7, find y. y =    \n10.) Equation: y = 32x gallons / cost ($)  \nIf x = 8, find y. y =    \n7.) A recipe uses 3 cups of oats per batch.  \nEquation:    \n8.) A faucet drips 2/5 of a gallon every hour.  \nEquation:    \n11.) Equation: y = 5x $ earned / hours worked If y = 35, find x. x =    \n12.) Equation: y = 23x minutes / miles If x = 15, find y. y =    \nPart 4—Word Problems  \n13.) A worker earns $12 per hour. Write an equation. How much for 9 hours?  \nEquation:   Answer:    \n14.) A car uses 1/4 gallon per mile. Write an equation. How much gas for 60 miles?  \nEquation:   Answer:    \n15.) A recipe uses 2/3 cup of sugar per dozen cookies. How much sugar for 5 dozen?  \nEquation:   Answer:    \n16.) Challenge Problem  \nLorenzo earns money working at a cafe at a constant rate. He earned $42 for 6 hours.  \na) Find k (his hourly rate) . Write the equation y = kx:    \nb) How many hours does he need to work to earn $91? 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—Tables:  \n1.) k = 5  \n2.) k = 32  \ny = 5x  \n3 y = x  \n2  \nPart 2—Descriptions:  \n5.) d = 60t (k = 60)  \n6.) c = 5/4 p (k = 54)  \nPart 3—Find the Missing Value:  \n9.) y = 28  \n10.) y = 12  \nPart 4—Word Problems:  \n13.) y = 12x y = 12(9) = $108  \n14.) y = 1/4 x y = 1/4(60) = 15 gallons  \n15.) y = 2/3 x y = 2/3(5) = 10/3 = 3⅓ cups  \n16.) Challenge:  \na) k = 42 ÷ 6 = $7/hr. Equation: y = 7x  \nb) 91 = 7x → x = 91 ÷ 7 = 13 hours  \n1 1  \n3.) k =  y = x 3 3  \n4.) k = 34 y = 34x  \n7.) y = 3x (k = 3)  \n8.) y = 2/5 x (k = 25)  \n11.) x = 7  \n12.) y = 10  \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)","cbCair7YFTt7Of5r","https://ap.wps.com/l/cbCair7YFTt7Of5r","pdf",1578014,"English","# Part 1—Find k from the Table, Write the Equation\n# Part 2—Write the Equation from the Description\n# Part 3—Use the Equation to Find the Missing Value\n# Part 4—Word Problems\n# Answer Key","[{\"question\":\"How do you find the constant of proportionality k in y = kx?\",\"answer\":\"When y is proportional to x, divide any y-value by its corresponding x-value: k = y ÷ x. Then use k to write the equation y = kx.\"},{\"question\":\"What steps should you follow to solve for a missing value using y = kx?\",\"answer\":\"Write the equation y = kx using the given k (from a table or description). Substitute the known x or y value, then solve for the unknown variable.\"},{\"question\":\"What do the word problems ask you to do?\",\"answer\":\"Translate real situations with constant rates into an equation y = kx, then answer questions such as cost for a number of hours, gallons for a distance, or sugar for a given number of cookies.\"}]","Writing Equations for Proportional Relationships (A) | PDF",1790138700,[146],{"page_no":8,"url":147,"width":148,"height":149},"https://res-academy.cache.wpscdn.com/upload/kdocshare/2026-11-08/41a28cc097957b4ebdaf0628fb382917.webp",983,1272]