{"id":317,"date":"2022-04-13T09:02:20","date_gmt":"2022-04-13T09:02:20","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=317"},"modified":"2025-08-20T01:37:28","modified_gmt":"2025-08-20T01:37:28","slug":"t-10-slope-intercept-form-write-an-equation-from-a-word-problem","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-10-slope-intercept-form-write-an-equation-from-a-word-problem\/","title":{"rendered":"T.10 Slope-intercept form: write an equation from a word problem"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#05006b;text-transform:uppercase\"><strong>Slope-intercept form: write an equation from a word problem<\/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=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwPqJWIPo\/3lpjYjEK7RRD1w0pReZqNA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwPqJWIPo&#x2F;3lpjYjEK7RRD1w0pReZqNA&#x2F;watch?utm_content=DAGwPqJWIPo&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.10 Slope-intercept form: write an equation from\u00a0a\u00a0word\u00a0problem<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-4565a8cbd03e1f5ef060035c9b5005a0\" style=\"color:#74008b\">Key notes<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-2acfd08e27d32a50489f6130c2bbe912\" style=\"color:#000060\"><strong>Slope-Intercept Form Recap<\/strong><\/h2>\n\n\n\n<p>The slope-intercept form of a line is: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>y=mx+b<\/strong><\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>m <\/strong>= slope (rate of change)<\/li>\n\n\n\n<li><strong>b<\/strong> = y-intercept (starting value)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-4dfca8570de6fbd33cfd378b48b97b59\" style=\"color:#000060\"><strong>Word Problems and What They Mean<\/strong><\/h2>\n\n\n\n<p>In real-life problems:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Slope (m)<\/strong> often represents the <strong>rate of change<\/strong> (how much<strong> y<\/strong> changes for each unit of<strong> x<\/strong>).<\/li>\n\n\n\n<li><strong>Y-intercept (b)<\/strong> often represents the <strong>initial value<\/strong> (when x=0).<\/li>\n\n\n\n<li><strong>x <\/strong>is usually the <strong>independent variable<\/strong> (time, distance, items, etc.).<\/li>\n\n\n\n<li><strong>y <\/strong>is usually the <strong>dependent variable<\/strong> (total cost, height, money earned, etc.).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-83d0ba5c1808cafa823be91cd890a160\" style=\"color:#000060\"><strong>Steps to Write an Equation from a Word Problem<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Identify the slope m<\/strong> from the rate given in the problem.<\/li>\n\n\n\n<li><strong>Identify the y-intercept b<\/strong>(starting amount or initial value).<\/li>\n\n\n\n<li>Write the equation in: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>y=mx+b<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Label the variables to match the problem\u2019s context.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-20a385a0dc8d73fb6ce56dabdf0c275f\" style=\"color:#000060\"><strong> Example 1 \u2013 Direct Information<\/strong><\/h2>\n\n\n\n<p>A taxi charges a base fare of $5 plus $2 for every mile.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Base fare = b=5 (starting cost)<\/li>\n\n\n\n<li>Rate = m=2 (cost per mile)<\/li>\n<\/ul>\n\n\n\n<p>Equation:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>y=2x+5<\/strong><\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>x<\/strong> = miles driven<\/li>\n\n\n\n<li><strong>y<\/strong>= total cost in dollars<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-5697c8f87c2abe8377882d2c8061532d\" style=\"color:#000060\"><strong> Example 2 \u2013 Given Two Situations<\/strong><\/h2>\n\n\n\n<p>A gym charges a joining fee plus a monthly fee. You pay $50 after 1 month and $80 after 4 months.<br>Step 1: Find slope mmm<br>Points: (1, 50) and (4, 80)<\/p>\n\n\n\n<p class=\"has-text-align-center\">m=80\u221250\/4\u22121=30\/3=10<\/p>\n\n\n\n<p>Step 2: Find bbb using (1, 50)<\/p>\n\n\n\n<p class=\"has-text-align-center\">50=10(1)+b<\/p>\n\n\n\n<p class=\"has-text-align-center\">b=40<\/p>\n\n\n\n<p>Step 3: Write equation<\/p>\n\n\n\n<p class=\"has-text-align-center\">y=10x+40<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>x <\/strong>= number of months<\/li>\n\n\n\n<li><strong>y<\/strong> = total cost in dollars<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-63b66385b8e8fa2a8f0be21606643db5\" style=\"color:#000060\"><strong>Special Tips<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u201cStarting at\u201d<\/strong> or <strong>\u201cinitially\u201d<\/strong> usually gives <strong>b<\/strong>.<\/li>\n\n\n\n<li><strong>\u201cPer\u201d<\/strong>, <strong>\u201ceach\u201d<\/strong>, <strong>\u201cevery\u201d<\/strong> usually gives<strong> m<\/strong>.<\/li>\n\n\n\n<li>If given two data points, find mmm first, then <strong>b<\/strong>.<\/li>\n\n\n\n<li>Always define what<strong> x<\/strong> and<strong> y<\/strong> represent.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-0f342ac45fa25a567324a19ff2936acb\" style=\"color:#000060\"><strong> Practice Problems<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>A streaming service charges $8 per month and a one-time sign-up fee of $12. Write the equation for the total cost <strong>y<\/strong> after <strong>x<\/strong> months.<\/li>\n\n\n\n<li>A plumber charges $60 for the first hour and $40 for each additional hour. Write the equation for the total cost after <strong>x<\/strong> hours.<\/li>\n\n\n\n<li>You have $100 in your savings account and deposit $15 each week. Write the equation for the total savings after<strong> x <\/strong>weeks.<\/li>\n\n\n\n<li>A phone company charges $25 per month and a $50 activation fee. Write the cost equation.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/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<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#e6f7cc\"><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-foreground-color has-text-color has-link-color wp-elements-9e310cd2fd03d7742f4f578ebfc29df4\"><strong>Irma uses 4 centimeters of tape for every present she wraps. Write an equation that shows the relationship between the number of presents&nbsp;<em>x<\/em>&nbsp;and the tape used&nbsp;<em>y<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1728089b0aa7d8360c6e807e18b42674\" style=\"color:#b00012\">Write your answer as an equation with&nbsp;y&nbsp;first, followed by an equals sign.<\/p>\n<\/div><\/div>\n\n\n\n<p>Make a chart.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1684232378681_315\" class=\"wp-block-table\"><table><tbody><tr><td>Number of presents (<em>x<\/em>)<\/td><td>Calculation of tape used (<em>y<\/em>)<\/td><td>Tape used (<em>y<\/em>)<\/td><\/tr><tr><td>1<\/td><td>4(1)<\/td><td>4<\/td><\/tr><tr><td>2<\/td><td>4(2)<\/td><td>8<\/td><\/tr><tr><td>3<\/td><td>4(3)<\/td><td>12<\/td><\/tr><tr><td><em>x<\/em><\/td><td>4(<em>x<\/em>)<\/td><td><strong>4<em>x<\/em><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Find the pattern:&nbsp;<em>y<\/em>&nbsp;is 4 times&nbsp;<em>x<\/em>.<\/p>\n\n\n\n<p>Write this relationship as an equation.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>y<\/em>&nbsp;is 4 times&nbsp;<em>x<\/em><\/td><\/tr><tr><td>&nbsp;&nbsp;\u2193&nbsp;&nbsp;<\/td><\/tr><tr><td><em>y<\/em>&nbsp;= 4<em>x<\/em><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#ead3f7\"><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-foreground-color has-text-color has-link-color wp-elements-a94e36378e11ccaeb25ec53418b9bab5\"><strong>Kurt jars 4 liters of jam every day. Write an equation that shows the relationship between the days&nbsp;<em>x<\/em>&nbsp;and the jam made&nbsp;<em>y<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1728089b0aa7d8360c6e807e18b42674\" style=\"color:#b00012\">Write your answer as an equation with&nbsp;y&nbsp;first, followed by an equals sign.<\/p>\n<\/div><\/div>\n\n\n\n<p>Make a chart.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1684232453579_314\" class=\"wp-block-table\"><table><tbody><tr><td>Days (<em>x<\/em>)<\/td><td>Calculation of jam made (<em>y<\/em>)<\/td><td>Jam made (<em>y<\/em>)<\/td><\/tr><tr><td>1<\/td><td>4(1)<\/td><td>4<\/td><\/tr><tr><td>2<\/td><td>4(2)<\/td><td>8<\/td><\/tr><tr><td>3<\/td><td>4(3)<\/td><td>12<\/td><\/tr><tr><td><em>x<\/em><\/td><td>4(<em>x<\/em>)<\/td><td><strong>4<em>x<\/em><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Find the pattern:&nbsp;<em>y<\/em>&nbsp;is 4 times&nbsp;<em>x<\/em>.<\/p>\n\n\n\n<p>Write this relationship as an equation.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>y<\/em>&nbsp;is 4 times&nbsp;<em>x<\/em><\/td><\/tr><tr><td>&nbsp;&nbsp;\u2193&nbsp;&nbsp;<\/td><\/tr><tr><td><em>y<\/em>&nbsp;= 4<em>x<\/em><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f0e69f\"><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-foreground-color has-text-color has-link-color wp-elements-dcfd837ee218f1b96da53155b2fa45ec\"><strong>Hunter takes 6 quizzes each week. Write an equation that shows the relationship between the number of weeks&nbsp;<em>x<\/em>&nbsp;and the total number of quizzes&nbsp;<em>y<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1728089b0aa7d8360c6e807e18b42674\" style=\"color:#b00012\">Write your answer as an equation with&nbsp;y&nbsp;first, followed by an equals sign.<\/p>\n<\/div><\/div>\n\n\n\n<p>Make a chart.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1684232523907_314\" class=\"wp-block-table\"><table><tbody><tr><td>Number of weeks (<em>x<\/em>)<\/td><td>Calculation of total number of quizzes (<em>y<\/em>)<\/td><td>Total number of quizzes (<em>y<\/em>)<\/td><\/tr><tr><td>1<\/td><td>6(1)<\/td><td>6<\/td><\/tr><tr><td>2<\/td><td>6(2)<\/td><td>12<\/td><\/tr><tr><td>3<\/td><td>6(3)<\/td><td>18<\/td><\/tr><tr><td><em>x<\/em><\/td><td>6(<em>x<\/em>)<\/td><td><strong>6<em>x<\/em><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Find the pattern:&nbsp;<em>y<\/em>&nbsp;is 6 times&nbsp;<em>x<\/em>.<\/p>\n\n\n\n<p>Write this relationship as an equation.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>y<\/em>&nbsp;is 6 times&nbsp;<em>x<\/em><\/td><\/tr><tr><td>&nbsp;&nbsp;\u2193&nbsp;&nbsp;<\/td><\/tr><tr><td><em>y<\/em>&nbsp;= 6<em>x<\/em><\/td><\/tr><\/tbody><\/table><\/figure>\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\/78185\/581\/795\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122.png\" alt=\"\" class=\"wp-image-8066\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122-150x150.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\/76986\/703\/762\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-131.png\" alt=\"\" class=\"wp-image-8068\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-131.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-131-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-131-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Slope-intercept form: write an equation from a word problem T.10 Slope-intercept form: write an equation from\u00a0a\u00a0word\u00a0problem by Delta publications Key notes Slope-Intercept Form Recap The slope-intercept form of a line is: y=mx+b where: Word Problems and What They Mean In real-life problems: Steps to Write an Equation from a Word Problem y=mx+b Example 1 \u2013<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-10-slope-intercept-form-write-an-equation-from-a-word-problem\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.10 Slope-intercept form: write an equation from a word problem&#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-317","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/317","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=317"}],"version-history":[{"count":17,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/317\/revisions"}],"predecessor-version":[{"id":17550,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/317\/revisions\/17550"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}