[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-274679-105":59,"doc-detail-274679-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","graphing-linear-inequalities-practice-problems-and-answer-keys","Graphing Linear Inequalities - Practice Problems and Answer Keys","","Graphing Linear Inequalities explains how to represent two-variable inequalities on a coordinate plane by first drawing the boundary line and choosing whether it is dashed or solid based on the inequality symbol. It emphasizes testing a point such as (0, 0) to determine which side of the boundary to shade as the solution region. The material includes multiple practice problems that ask students to graph inequalities, identify whether a given point satisfies the inequality, and complete word problems.",{"@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/graphing-linear-inequalities-practice-problems-and-answer-keys/274679/",{"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/graphing-linear-inequalities-practice-problems-and-answer-keys/274679.png","ImageObject",300,407,{"name":92,"@type":93},"Miles","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-24","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you decide whether the boundary line is dashed or solid?","Question",{"text":113,"@type":114},"Use a dashed line when the inequality is \u003C or > (the line is not included), and a solid line when the inequality is ≤ or ≥ (the line is included).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How can you determine which side of the boundary to shade?",{"text":118,"@type":114},"Shade the side that makes the inequality true by testing a point such as (0, 0). If it works, shade that side; otherwise shade the opposite side.",{"name":120,"@type":111,"acceptedAnswer":121},"Do you shade above or below the line for y > or y ≤?",{"text":122,"@type":114},"For y > or y ≥, shade above the line. For y \u003C or y ≤, shade below the line.","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},274679,1789481349,{"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":39,"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":130,"read_time":46},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Practice 􀀏 Progress 􀀏 Succeed | SHSAT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nGraphing Linear Inequalities  \n\n| Name:   | D | ate:   | S | core:   / 18 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nTo graph a two-variable inequality, 􀀂rst draw the boundary line: use a dashed line for \u003C or > (the line isnot included) and a solid line for 􀀔 or 􀀕 . Then shade the side that makes it true – test a point such as (0, 0): if it works, shade its side. For y > or y 􀀕 shade above the line; for y \u003C or y 􀀔 shade below.  \n▷ Example: Describe the graph of y \u003C x + 2, and test whether (0, 0) is a solution. Work: The symbol is \u003C, so the boundary y = x + 2 is dashed. Test (0, 0): 0 \u003C 0 + 2 means 0 \u003C 2, which is true, so (0, 0) is a solution and you shade its side (below the line) . ⋆ Answer: dashed;(0, 0) is a solution  \ny \u003C x + 2: dashed line, shade below.  \n♦ Practice Problems  \nGraph each inequality on the coordinate plane, then answer the question about its solution region.  \n1. Graph y \u003C x + 2 . Is (0, 0) a solution?  \n2. Graph y > 2x. Is (1, 5) a solution?  \n3. Graph y 􀀔 x. Is (2, 1) a solution?  \n4. Graph y > x + 1 . Is (0, 0) a solution?  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | SHSAT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n9. Graph y 􀀕 x + 2 . Is (􀀀1, 0) a solution?  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n2  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | SHSAT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n13. Graph y > x 􀀀 3. Is the boundary solid or dashed?  \n14. Graph y \u003C 2x. Shade above or below the line?  \n♦ Word Problems  \n15. For the inequality y 􀀕 3x 􀀀 1, is the boundary line solid or dashed?  \n16. Test the point (0, 0) in y > x + 4 . Is it a solution?  \n17. For y 􀀔 x, do you shade above or below the boundary line?  \n18. Is the point (2, 2) a solution of y 􀀕 2x 􀀀 2?  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n3  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | SHSAT Math  \nAnswer Keys  \n [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](Effor","cbCaisErByhQ47CD","https://ap.wps.com/l/cbCaisErByhQ47CD","pdf",332127,"English","# Quick Review and Helpful Hints\n## How to draw boundary lines\n## How to test a point and shade the solution region\n# Practice Problems\n## Graphing and checking solutions\n# Word Problems\n## Boundary type and point tests\n# Answer Keys","[{\"question\":\"How do you decide whether the boundary line is dashed or solid?\",\"answer\":\"Use a dashed line when the inequality is \\u003c or \\u003e (the line is not included), and a solid line when the inequality is ≤ or ≥ (the line is included).\"},{\"question\":\"How can you determine which side of the boundary to shade?\",\"answer\":\"Shade the side that makes the inequality true by testing a point such as (0, 0). If it works, shade that side; otherwise shade the opposite side.\"},{\"question\":\"Do you shade above or below the line for y \\u003e or y ≤?\",\"answer\":\"For y \\u003e or y ≥, shade above the line. For y \\u003c or y ≤, shade below the line.\"}]","Graphing Linear Inequalities - Practice Problems and Answer Keys | PDF"]