{"id":298,"date":"2022-04-13T08:59:37","date_gmt":"2022-04-13T08:59:37","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=298"},"modified":"2025-08-18T10:56:44","modified_gmt":"2025-08-18T10:56:44","slug":"t-1-identify-linear-equations","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-1-identify-linear-equations\/","title":{"rendered":"T.1 Identify linear equations"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Identify linear equations<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"padding:56.25% 0 0 0;position:relative;\"><iframe src=\"https:\/\/player.vimeo.com\/video\/1110912092?badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write; encrypted-media; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" style=\"position:absolute;top:0;left:0;width:100%;height:100%;\" title=\"T.1 Identify linear equations\"><\/iframe><\/div><script src=\"https:\/\/player.vimeo.com\/api\/player.js\"><\/script>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-0168950823342d5d0ea6c3655d119723\" style=\"color:#000060\"><strong>What is a Linear Equation?<\/strong><\/h3>\n\n\n\n<p>A <strong>linear equation<\/strong> is an equation in which the highest power of the variable(s) is <strong>1<\/strong>.<\/p>\n\n\n\n<p>Its graph is always a <strong>straight line<\/strong>.<\/p>\n\n\n\n<p>General form for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>One variable:<\/strong> ax + b = 0<\/li>\n\n\n\n<li><strong>Two variables:<\/strong> ax + by + c = 0<\/li>\n\n\n\n<li><strong>Three variables:<\/strong> ax + by + cz + d = 0<br>where a,b,c,d are real numbers and a,b, c are not all zero.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-af7ef79d27a20702a45d86bd1c49b19b\" style=\"color:#000060\"><strong>Identifying Linear Equations<\/strong><\/h3>\n\n\n\n<p>An equation is <strong>linear<\/strong> if:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The variables have <strong>no exponents<\/strong> greater than 1.<\/li>\n\n\n\n<li>The variables are <strong>not multiplied together<\/strong>.<\/li>\n\n\n\n<li>The variables appear with <strong>constant coefficients<\/strong>.<\/li>\n\n\n\n<li>No term involves roots, fractions of the variable, or trigonometric functions of the variable.<\/li>\n<\/ul>\n\n\n\n<p><strong>Examples of Linear Equations:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2x + 5 = 0 \u2014 One variable<\/li>\n\n\n\n<li>3x \u2212 4y + 7 = 0 \u2014 Two variables<\/li>\n\n\n\n<li>x + y + z = 6 \u2014 Three variables<\/li>\n<\/ul>\n\n\n\n<p><strong>Not Linear:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x<sup>2<\/sup> + 2x + 3 = 0 (power 2)<\/li>\n\n\n\n<li>xy + 2 = 0 (product of variables)<\/li>\n\n\n\n<li>x + y = 4 (variable under root)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-52a7318ffecac57b157445c6da8af55f\" style=\"color:#000060\"><strong>Key Characteristics<\/strong><\/h3>\n\n\n\n<p><strong>Degree:<\/strong> 1 (highest power of the variable is 1)<\/p>\n\n\n\n<p><strong>Graph:<\/strong> Straight line<\/p>\n\n\n\n<p><strong>Solutions:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One variable \u2192 single value<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two variables \u2192 infinite solutions forming a line<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Three variables \u2192 plane intersection lines<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-6fe4d1024f7ee7a7ec7299fec9bfb61d\" style=\"color:#000060\"><strong>Examples for Practice<\/strong><\/h3>\n\n\n\n<p><strong>Linear:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5p \u2212 3q = 9<\/li>\n\n\n\n<li>0.5x + 2y \u2212 1 = 0<\/li>\n<\/ul>\n\n\n\n<p><strong>Not Linear:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2x<sup>2<\/sup> \u2212 3y = 5<\/li>\n\n\n\n<li>xy = 10<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-04e017087784ffc309e5d698018f9530\" style=\"color:#000060\"><strong>Quick Tip to Identify<\/strong><\/h3>\n\n\n\n<p>Ask yourself:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Are there <strong>only variables to the power 1<\/strong>?<\/li>\n\n\n\n<li>Are the variables <strong>not multiplied<\/strong> with each other?<\/li>\n\n\n\n<li>Are there <strong>no roots or reciprocals<\/strong> of variables?<\/li>\n<\/ul>\n\n\n\n<p>If all answers are <strong>YES<\/strong>, it\u2019s a <strong>linear equation<\/strong>.<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#96eeee\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-4c0f6a5bc3024772fd218de40794ac83\" style=\"color:#b00012\">The&nbsp;graph shows a function. Is the function linear or&nbsp;nonlinear?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__3_-removebg-preview.png\" alt=\"\" class=\"wp-image-11487\" style=\"width:426px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Linear<\/strong><\/li>\n\n\n\n<li><strong>Non-linear<\/strong><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p><br>To&nbsp;determine whether the function is linear or nonlinear, see whether the graph is a straight&nbsp;line.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__3_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-11490\" style=\"width:395px;height:auto\"\/><\/figure><\/div>\n\n\n<p>The&nbsp;graph is a straight&nbsp;line.<\/p>\n\n\n\n<p>So,&nbsp;the function is&nbsp;<strong>linear<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#e595ca\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-4c0f6a5bc3024772fd218de40794ac83\" style=\"color:#b00012\">The&nbsp;graph shows a function. Is the function linear or&nbsp;nonlinear?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__5_-removebg-preview.png\" alt=\"\" class=\"wp-image-11497\" style=\"width:370px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Linear <\/li>\n\n\n\n<li>Non-linear<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;determine whether the function is linear or nonlinear, see whether the graph is a straight&nbsp;line. <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__5_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-11498\" style=\"width:408px;height:auto\"\/><\/figure><\/div>\n\n\n<p>The&nbsp;graph is a straight&nbsp;line.<\/p>\n\n\n\n<p>So,&nbsp;the function is&nbsp;<strong>linear<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/77079\/268\/880\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-117.png\" alt=\"\" class=\"wp-image-8051\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-117.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-117-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-117-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76807\/844\/661\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-126.png\" alt=\"\" class=\"wp-image-8052\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-126.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-126-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-126-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Identify linear equations Key Notes: What is a Linear Equation? A linear equation is an equation in which the highest power of the variable(s) is 1. Its graph is always a straight line. General form for: Identifying Linear Equations An equation is linear if: Examples of Linear Equations: Not Linear: Key Characteristics Degree: 1 (highest<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-1-identify-linear-equations\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.1 Identify linear equations&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-298","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/298","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=298"}],"version-history":[{"count":25,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/298\/revisions"}],"predecessor-version":[{"id":17524,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/298\/revisions\/17524"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}