{"id":3483,"date":"2022-02-06T10:21:57","date_gmt":"2022-02-06T10:21:57","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=3483"},"modified":"2022-02-06T10:21:57","modified_gmt":"2022-02-06T10:21:57","slug":"writing-linear-equations","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/writing-linear-equations\/","title":{"rendered":"Writing Linear Equations"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Writing Linear Equations<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Write linear equations involving variables. This equation will be a linear combination of the two variables, and a constant can be present. When any linear equation is plotted on a graph, it will necessarily produce a straight line – hence the name: Linear equations.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Find the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope\">slope<\/a> using the formula <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\" alt=\"\\fn_phv m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\" align=\"absmiddle\" \/><br \/>\n2. Use the slope for m and the coordinates of either point (as <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;x_{1}\" alt=\"\\fn_phv x_{1}\" align=\"absmiddle\" \/> and <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y_{1}\" alt=\"\\fn_phv y_{1}\" align=\"absmiddle\" \/>) in the formula <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y-y_{1}=m(x-x_{1})\" alt=\"\\fn_phv y-y_{1}=m(x-x_{1})\" align=\"absmiddle\" \/><br \/>\n3. Simplify the equation and solve for <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y\" alt=\"\\fn_phv y\" align=\"absmiddle\" \/>.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">It costs $5 to mail a package weighing 2 kg. To mail a package weighing 3 kg, the shipping cost is $6.50.<br \/>\n<\/span><\/strong><strong>Write the linear equation that models the relationship between the weight of a package (x) and the shipping cost (y).<\/strong>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]The data points are (2 kg, $5) and (3 kg, $6.50).<br \/>\nTo find the slope, use the formula<br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\" alt=\"\\fn_phv m=\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;m=\\frac{6.5-5}{3-2}=\\frac{1.5}{1}\" alt=\"\\fn_phv m=\\frac{6.5-5}{3-2}=\\frac{1.5}{1}\" align=\"absmiddle\" \/><br \/>\nThen, Use the slope for m and the coordinates of either point (as <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;x_{1}\" alt=\"\\fn_phv x_{1}\" align=\"absmiddle\" \/> and <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y_{1}\" alt=\"\\fn_phv y_{1}\" align=\"absmiddle\" \/>) in the formula <img style=\"margin-top: 7px; margin-bottom: 7px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y-y_{1}=m(x-x_{1})\" alt=\"\\fn_phv y-y_{1}=m(x-x_{1})\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 7px; margin-bottom: 7px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y-5=1.5(x-2)\" alt=\"\\fn_phv y-5=1.5(x-2)\" align=\"absmiddle\" \/><br \/>\nSimplify the equation.<br \/>\n<img style=\"margin-top: 7px; margin-bottom: 7px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y-5=1.5x-3\" alt=\"\\fn_phv y-5=1.5x-3\" align=\"absmiddle\" \/><br \/>\nAdd 5 to both sides, and you get:<br \/>\n<img style=\"margin-top: 7px; margin-bottom: 7px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{\\color{Red}&space;y=1.5x+2}\" alt=\"\\fn_phv {\\color{Red} y=1.5x+2}\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Writing Linear Equations[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Write the equation of a line with a slope of \u2212<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{\\color{Teal}&space;\\frac{2}{5}}\" alt=\"\\fn_phv {\\color{Teal} \\frac{2}{5}}\" align=\"absmiddle\" \/>\u00a0that goes through the point (5,\u22121).<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-linear-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-3486 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-34.png\" alt=\"\" width=\"116\" height=\"46\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-linear-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Write the equation of the line that passes through A (2,5) and B (-2,3).<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-linear-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-3486 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-34.png\" alt=\"\" width=\"116\" height=\"46\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-linear-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">It costs $32 for 8 liters of gas. It costs $46 for 12 liters of gas.<\/span><\/strong><br \/>\n<strong>Write the linear equation that models the relationship between the number of liters (x) and the cost of gas (y).<\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-two-step-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-3486 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-34.png\" alt=\"\" width=\"116\" height=\"46\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-two-step-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Algebra<\/strong> \u2013 the branch of mathematics that involves expressions with variables.<\/p>\n<p><strong>Variable<\/strong> \u2013 a symbol that represents an unknown quantity.<\/p>\n<p><strong>Equation<\/strong> – In algebra an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.<\/p>\n<p>A <strong>linear equation<\/strong> is an equation that is written for two different variables.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/constant-rate-of-change\"><span style=\"color: #ed5600;\">Constant rate of Change<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope\"><span style=\"color: #ed5600;\">Slope<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-\"><span style=\"color: #ed5600;\">Direct Variation Equations (y = mx)<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope-intercept-form-of-an-equation\"><span style=\"color: #ed5600;\">Slope-intercept Form of an Equation<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/graphing-lines-using-intercepts\"><span style=\"color: #ed5600;\">Graphing Lines Using Intercepts<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635256449985{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-additon-and-subtraction\"><span style=\"color: #333399;\">Solve One-Step Equations by Addition and Subtraction<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-multipying-and-dividing\"><span style=\"color: #333399;\">Solve One-Step Equations by Multiplying and Dividing<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-equations-with-rational-coefficients\"><span style=\"color: #333399;\">Solve Equations with Rational Coefficients<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-two-step-equations\"><span style=\"color: #333399;\">Solve Two-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-complex-equations\"><span style=\"color: #333399;\">Solve Complex Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-equations-with-rational-coefficients\"><span style=\"color: #333399;\">Solve Equations with Rational Coefficients<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-two-step-equations\"><span style=\"color: #333399;\">Solve Two-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-substitution\"><span style=\"color: #333399;\">Solve Systems of Equations by Substitution<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\"><span style=\"color: #333399;\">Solve Systems of Equations by Elimination<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-systems\"><span style=\"color: #333399;\">Applications of Systems<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” 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link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Faddition|title:Addition||”][vc_btn title=”Algebra” color=”danger” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Falgebra|title:Algebra||”][vc_btn title=”Division” color=”violet” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Fdivision|title:Division||”][vc_btn title=”Functions and equations” color=”blue” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Ffunctions-and-equations|title:Functions%20and%20equations||”][vc_btn title=”Subtraction” color=”green” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Fsubtraction|title:Subtraction||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Writing Linear Equations [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Write linear equations involving variables. This equation will be a linear combination of the two variables, and a constant can be present. When any linear equation is plotted […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Writing Linear Equations | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/writing-linear-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Writing Linear Equations\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Writing Linear Equations [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Write linear equations involving variables. This equation will be a linear combination of the two variables, and a constant can be present. 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This equation will be a linear combination of the two variables, and a constant can be present. 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