{"id":168,"date":"2022-04-12T12:17:40","date_gmt":"2022-04-12T12:17:40","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=168"},"modified":"2024-11-28T07:52:02","modified_gmt":"2024-11-28T07:52:02","slug":"h-13-rate-of-change","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/h-13-rate-of-change\/","title":{"rendered":"H.13 Rate of change"},"content":{"rendered":"\n<h1 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Rate of change<\/strong><\/h1>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-aae0d72b0df05b1a7d05750bd97517d2\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-19de98fb6fb518241b9db3b308bfca19\" style=\"color:#000060\"><strong>1. Definition of Rate of Change<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>The rate of change refers to how one quantity changes in relation to another. It is often expressed as the ratio of the change in the dependent variable to the change in the independent variable.<\/li>\n\n\n\n<li>It can be represented mathematically as<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"545\" height=\"79\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-205.png\" alt=\"\" class=\"wp-image-19141\" style=\"width:421px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-205.png 545w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-205-300x43.png 300w\" sizes=\"auto, (max-width: 545px) 100vw, 545px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">where \u0394y is the change in the dependent variable (y), and \u0394x is the change in the independent variable (x).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-c263acf93cf28eae2650e993d8601a93\" style=\"color:#000060\"><strong>2. Common Examples of Rate of Change<\/strong><\/h3>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Speed<\/strong>: How distance changes with respect to time. Formula<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"270\" height=\"83\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-206.png\" alt=\"\" class=\"wp-image-19142\" style=\"width:226px;height:auto\"\/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\"><strong>Slope of a line<\/strong>: In a straight line, the rate of change of y with respect to x is represented by the slope (m):<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"200\" height=\"85\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-207.png\" alt=\"\" class=\"wp-image-19143\" style=\"width:162px;height:auto\"\/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">where (x1,y1) and (x2,y2) are two points on the line.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-b82ef6162351eaf18ca0188021c3409d\" style=\"color:#000060\"><strong>3. Calculating Rate of Change<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Formula for rate of change<\/strong>:\n<ul class=\"wp-block-list\">\n<li>If you are given two points, (x1,y1) and (x2,y2), the rate of change can be calculated using the formula:<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"63\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-208.png\" alt=\"\" class=\"wp-image-19149\"\/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\"><strong>Units of Rate of Change<\/strong>: Depending on the situation, rate of change is expressed in units such as meters per second (m\/s), kilometers per hour (km\/h), dollars per item, etc.<\/p>\n\n\n\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-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-5925a5d4635c0ded516dc1d490ee210c\" style=\"background-color:#affbc5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-98fb01442d032ac176a0c3091da9d077\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-84f8bfb67c70cf38a894aa5cbc9243fb\" style=\"color:#b00012\"><strong>\ud83d\udc49 Mrs.&nbsp;Green hosts an annual art contest for kids, and she keeps a record of the number of entries each&nbsp;year.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__64_-removebg-preview.png\" alt=\"\" class=\"wp-image-3509\" style=\"width:288px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__64_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__64_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__64_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p><strong>\ud83d\udc49 According&nbsp;to the table, what was the rate of change between 2010 and&nbsp;2014?<\/strong><\/p>\n\n\n\n<p><strong>___ entries&nbsp;per&nbsp;year<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Plug&nbsp;the numbers into the formula for rate of change and&nbsp;simplify.<\/li>\n\n\n\n<li>Rate&nbsp;of&nbsp;change = change&nbsp;in&nbsp;value\/change&nbsp;in&nbsp;time<\/li>\n\n\n\n<li>= 69 entries \u2013 65 entries \/ 2014 \u2013 2010<\/li>\n\n\n\n<li>= 69 entries \u2013 65 entries \/ 4 years<\/li>\n\n\n\n<li>= 4 entries \/ 4 years<\/li>\n\n\n\n<li>= 1 entry&nbsp;per&nbsp;year<\/li>\n\n\n\n<li>The rate of change between 2010 and 2014 was 1 entry per year.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-e1b49717cf57f98c9ce1eeefae4fa0df\" style=\"background-color:#8ad7fe\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-d97ffb314d01ce3243e548983c2a058e\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-dd84a520897fbddb0a030140b6538dd8\" style=\"color:#b00012\"><strong>\ud83d\udc49 Cameron&nbsp;kept track of how long it took to finish his homework each&nbsp;day.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__65_-removebg-preview.png\" alt=\"\" class=\"wp-image-3512\" style=\"width:341px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__65_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__65_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__65_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p><strong>\ud83d\udc49 According&nbsp;to the table, what was the rate of change between Monday and&nbsp;Thursday?<\/strong><\/p>\n\n\n\n<p><strong>_____ minutes&nbsp;per&nbsp;day<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Plug&nbsp;the numbers into the formula for rate of change and&nbsp;simplify.<\/li>\n\n\n\n<li>Rate&nbsp;of&nbsp;change = change&nbsp;in&nbsp;value\/change&nbsp;in&nbsp;time<\/li>\n\n\n\n<li>= 52 minutes \u2013 43 minutes \/ 3 days<\/li>\n\n\n\n<li>= 9 minutes \/ 3 days<\/li>\n\n\n\n<li>= 3 minutes&nbsp;per&nbsp;day<\/li>\n\n\n\n<li>The rate of change between Monday and Thursday was 3 minutes per day.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-2b985f8c442ae14c62b819c29c2d2496\" style=\"background-color:#eaf293\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-2682db835f65b4166a9b5effe0f2680b\" style=\"color:#b00012\"><strong>\ud83d\udc49 A&nbsp;restaurant&#8217;s average food preparation time was tracked from day to day as part of an efficiency improvement&nbsp;program.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__63_-removebg-preview.png\" alt=\"\" class=\"wp-image-3504\" style=\"width:427px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__63_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__63_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__63_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p><strong>\ud83d\udc49 According&nbsp;to the graph, what was the rate of change between Friday and&nbsp;Saturday?<\/strong><\/p>\n\n\n\n<p><strong>_____ minutes&nbsp;per&nbsp;day<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Plug&nbsp;the numbers into the formula for rate of change and&nbsp;simplify.<\/li>\n\n\n\n<li>Rate&nbsp;of&nbsp;change = change&nbsp;in&nbsp;value\/change&nbsp;in&nbsp;time<\/li>\n\n\n\n<li>= 43 minutes \u2013 41 minutes \/ 1 day<\/li>\n\n\n\n<li>= 2 minutes \/ 1 day<\/li>\n\n\n\n<li>= 2 minutes&nbsp;per&nbsp;day<\/li>\n\n\n\n<li>The rate of change between Friday and Saturday was 2 minutes per day.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice! \ud83d\udd8a\ufe0f<\/strong><\/p>\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\/81278\/102\/866\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318.png\" alt=\"\" class=\"wp-image-9666\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-318-150x150.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\/81431\/966\/967\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326.png\" alt=\"\" class=\"wp-image-9667\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-326-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Rate of change Key Notes : 1. Definition of Rate of Change where \u0394y is the change in the dependent variable (y), and \u0394x is the change in the independent variable (x). 2. Common Examples of Rate of Change Slope of a line: In a straight line, the rate of change of y with respect<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/h-13-rate-of-change\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.13 Rate of change&#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-168","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/168","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=168"}],"version-history":[{"count":23,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/168\/revisions"}],"predecessor-version":[{"id":19151,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/168\/revisions\/19151"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}