{"id":172,"date":"2022-04-12T12:21:23","date_gmt":"2022-04-12T12:21:23","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=172"},"modified":"2024-11-28T09:01:30","modified_gmt":"2024-11-28T09:01:30","slug":"h-14-constant-rate-of-change","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/h-14-constant-rate-of-change\/","title":{"rendered":"H.14 Constant rate of change"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Constant rate of change<\/strong><\/h2>\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<p class=\"has-text-color has-link-color has-large-font-size wp-elements-c2aeaee71283b37069e7e4cfd20b598e\" style=\"color:#000060\"><strong>Definition:<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>The <strong>constant rate of change<\/strong> refers to the rate at which one quantity changes in relation to another in a linear relationship. It is the same throughout the entire interval or period being measured.<\/li>\n\n\n\n<li>It is often described as the <strong>slope<\/strong> of a line on a graph.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-540d5d71ba7c6bb1200ba35a9adabfbd\" style=\"color:#000060\"><strong>Formula for Constant Rate of Change:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">The formula to calculate the constant rate of change (or slope) is:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"386\" height=\"54\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-209.png\" alt=\"\" class=\"wp-image-19156\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-209.png 386w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-209-300x42.png 300w\" sizes=\"auto, (max-width: 386px) 100vw, 386px\" \/><\/figure><\/div>\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Where:<\/strong><\/li>\n<\/ul>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>\u0394y is the change in the dependent variable (vertical change).<\/li>\n\n\n\n<li>\u0394x is the change in the independent variable (horizontal change).<\/li>\n<\/ul>\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-background has-large-font-size\" style=\"background-color:#bfef9f\"><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-ec67ad3133339d7477160cbc3b59a39b\" style=\"color:#b00012\"><strong>\ud83d\udc49 This graph shows how the time required to ring up a customer is related to the number of items being purchased.<\/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-68.png\" alt=\"\" class=\"wp-image-3526\" style=\"width:347px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-68.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-68-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-68-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p><strong>\ud83d\udc49 What is the rate of change?<\/strong><\/p>\n\n\n\n<p><strong>Write your answer as a decimal or integer.<\/strong><\/p>\n\n\n\n<p><strong>_____ &nbsp;seconds per item<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>\u2708\ufe0f Find any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-70.png\" alt=\"\" class=\"wp-image-3525\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-70.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-70-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-70-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Two points on the line are&nbsp;(0, 20)&nbsp;and&nbsp;(50, 50).&nbsp;Put those points into the slope formula.<\/li>\n\n\n\n<li>slope = change in y \/ change in&nbsp;<em>x<\/em><\/li>\n\n\n\n<li>= 50 \u2212 20 \/ 50 \u2212 0 &#8212;&#8212;-&gt; <em>Plugin (<\/em><strong><em>0<\/em><\/strong><em>,&nbsp;<\/em><strong><em>20<\/em><\/strong><em>) and (<\/em><strong><em>50<\/em><\/strong><em>,&nbsp;<\/em><strong><em>50<\/em><\/strong><em>)<\/em><\/li>\n\n\n\n<li>= 30\/50 &#8212;&#8212;-&gt; Subtract<\/li>\n\n\n\n<li>= 3\/5 &#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>= 0.6 &#8212;&#8212;-&gt; <em>Write as a decimal<\/em><\/li>\n\n\n\n<li>The slope is 0.6. The rate of change is 0.60 seconds per item.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f4e6bd\"><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-c444108fc1d95318a3c85324c166faf8\" style=\"color:#b00012\"><strong>This graph shows how the number of flowers Marcy can have in her garden is related to the number of seed packets she purchases.<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-72.png\" alt=\"\" class=\"wp-image-3531\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-72.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-72-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-72-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p><strong>\ud83d\udc49 What is the rate of change?<\/strong><\/p>\n\n\n\n<p><strong>Write your answer as a decimal or integer.<\/strong><\/p>\n\n\n\n<p><strong>_____ &nbsp;flowers per seed packet<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>\u2708\ufe0f Find any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-73.png\" alt=\"\" class=\"wp-image-3533\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-73.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-73-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled-design-73-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Two points on the line are&nbsp;(0, 10)&nbsp;and&nbsp;(20, 40).&nbsp;Put those points into the slope formula.<\/li>\n\n\n\n<li>slope = change in y \/ change in&nbsp;<em>x<\/em><\/li>\n\n\n\n<li>= 40 \u2212 10 \/ <strong>20<\/strong>&nbsp;\u2212&nbsp;<strong>0<\/strong> &#8212;&#8212;-&gt; <em>Plugin (<\/em><strong><em>0<\/em><\/strong><em>,&nbsp;<\/em><strong><em>10<\/em><\/strong><em>) and (<\/em><strong><em>20<\/em><\/strong><em>,&nbsp;<\/em><strong><em>40<\/em><\/strong><em>)<\/em><\/li>\n\n\n\n<li>= 30\/20 &#8212;&#8211;&gt; Subtract<\/li>\n\n\n\n<li>= 3\/2 &#8212;&#8212;&gt; Simplify<\/li>\n\n\n\n<li>= 1.5 &#8212;&#8212;-&gt; Write as a decimal<\/li>\n\n\n\n<li>The slope is 1.5. The rate of change is 1.50 flowers per seed packet.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bcfab8\"><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-d0317e624cc5dda4cd2ec8b62249417b\" style=\"color:#b00012\"><strong>\ud83d\udc49 This graph shows how the number of pictures Gina has taken so far this year is related to the number of days she spends on holiday.<\/strong><\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__66_-removebg-preview.png\" alt=\"\" class=\"wp-image-3519\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__66_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__66_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__66_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p><strong>\ud83d\udc49 What is the rate of change?<\/strong><\/p>\n\n\n\n<p><strong>Write your answer as a decimal or integer.<\/strong><\/p>\n\n\n\n<p><strong>_______ &nbsp;pictures per day<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>\u2708\ufe0f Find any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__67_-removebg-preview.png\" alt=\"\" class=\"wp-image-3520\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__67_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__67_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__67_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Two points on the line are&nbsp;(0, 2)&nbsp;and&nbsp;(1, 4).&nbsp;Put those points into the slope formula.<\/li>\n\n\n\n<li>slope = change in y \/ change in x<\/li>\n\n\n\n<li>= 4 \u2212 2 \/ 1 \u2212 0 &#8212;&#8212;&gt; <em>Plugin (<\/em><strong><em>0<\/em><\/strong><em>,&nbsp;<\/em><strong><em>2<\/em><\/strong><em>) and (<\/em><strong><em>1<\/em><\/strong><em>,&nbsp;<\/em><strong><em>4<\/em><\/strong><em>)<\/em><\/li>\n\n\n\n<li>&nbsp;=&nbsp;2\/1 &#8212;&#8212;&gt; Subtract<\/li>\n\n\n\n<li>= 2 &#8212;&#8211;&gt; Simplify<\/li>\n\n\n\n<li>The slope is 2. The rate of change is 2 pictures per day.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice! \ud83d\udd8a\ufe0f<\/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\/81280\/414\/310\"><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\"><div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/wordwall.net\/play\/81433\/406\/878\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-2-2.png\" alt=\"\" class=\"wp-image-3630\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-2-2.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-2-2-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Worksheet-1-2-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure><\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Constant rate of change Key Notes : Definition: Formula for Constant Rate of Change: Learn with an example \ud83d\udc49 This graph shows how the time required to ring up a customer is related to the number of items being purchased. \ud83d\udc49 What is the rate of change? Write your answer as a decimal or integer.<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/h-14-constant-rate-of-change\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.14 Constant 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-172","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\/172","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=172"}],"version-history":[{"count":17,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/172\/revisions"}],"predecessor-version":[{"id":19157,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/172\/revisions\/19157"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}