{"id":28728,"date":"2023-05-05T07:00:53","date_gmt":"2023-05-05T07:00:53","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=28728"},"modified":"2023-11-15T16:27:58","modified_gmt":"2023-11-15T16:27:58","slug":"slope-of-parallel-line-formula-derivation-example","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines","title":{"rendered":"Slope of Parallel Line: Formula, Derivation, Example"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-1b5c8549-5e7b-41cb-9027-52bae2588f45\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines#0-what-is-the-slope-of-parallel-lines>What Is the Slope of Parallel Lines?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines#1-why-is-the-slope-of-parallel-lines-equal>Why Is the Slope of Parallel Lines Equal?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines#2-how-to-identify-parallel-lines>How to Identify Parallel Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines#9-solved-examples-on-slope-of-parallel-lines>Solved Examples on Slope of Parallel Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines#10-practice-problems-on-slope-of-parallel-lines>Practice Problems on Slope of Parallel Lines<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines#11-frequently-asked-questions-on-slope-of-parallel-lines>Frequently Asked Questions on Slope of Parallel Lines<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-slope-of-parallel-lines\">What Is the Slope of Parallel Lines?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>The slope of parallel lines is always equal.<\/strong> <strong>Parallel lines have the same slope because their rise over run ratio is equal. They make an equal angle with the positive x-axis.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">In geometry, parallel lines can be defined as two lines in the same plane that never meet and are at equal distance. The slope of a line is defined as the rise over run ratio or the ratio of the change in vertical distance over the change in the horizontal distance.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If we have two parallel lines with slopes $m_1$ and $m_2$, then $m_1 = m_2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Conversely, if the slopes of two lines are equal, then the lines are parallel to each other.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"592\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/the-parallel-lines-slope.png\" alt=\"The parallel lines slope\" class=\"wp-image-35802\" title=\"The parallel lines slope\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/the-parallel-lines-slope.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/the-parallel-lines-slope-300x286.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-like-fractions-using-number-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_like_frac_sum_upto_1_nl_pt.png\" alt=\"Add Like Fractions using Number Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Like Fractions using Number Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-pairs-of-parallel-sides-in-shapes-and-choose-the-correct-answer\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_count_parallel_2d_shape_pt.png\" alt=\"Count Pairs of Parallel Sides in Shapes and Choose the Correct Answer Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Pairs of Parallel Sides in Shapes and Choose the Correct Answer Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/divide-using-number-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_divide_nl_pt.png\" alt=\"Divide using Number Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Divide using Number Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-parallel-sides\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_parallel_sides_1_pt.png\" alt=\"Find Parallel Sides Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Parallel Sides Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-fractions-on-number-lines\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" 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class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_rhombus_parallelogram_pt.png\" alt=\"Identify Kite, Rhombuses and Parallelograms Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Kite, Rhombuses and Parallelograms Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-lines-line-segments-rays-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" 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Parallel and Perpendicular Lines Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Parallel and Perpendicular Lines Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-parallel-sides\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_parallel_sides_2_pt.png\" alt=\"Identify Parallel Sides Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Parallel Sides Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-parallel-sides-in-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_parallel_2d_shape_pt.png\" alt=\"Identify Parallel Sides in Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Parallel Sides in Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-why-is-the-slope-of-parallel-lines-equal\">Why Is the Slope of Parallel Lines Equal?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In geometry, two or more coplanar lines that never intersect and are equidistant are parallel lines. As parallel lines always rise and run at the same rate, they never intersect and have the same slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Two parallel lines have the same slope but different y-intercepts. If they have the same y-intercept, they will coincide.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Slope of parallel lines examples:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: <\/strong>Consider two lines having the slope of $\\frac{3}{5}$. Their graph shows that they have the same rise over run ratio. These lines are parallel.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"736\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rise-over-run-ratio-and-slope-of-parallel-lines.png\" alt=\"Rise over run ratio and slope of parallel lines\" class=\"wp-image-35803\" title=\"Rise over run ratio and slope of parallel lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rise-over-run-ratio-and-slope-of-parallel-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rise-over-run-ratio-and-slope-of-parallel-lines-253x300.png 253w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: <\/strong>Consider the lines $y = 2x + 3$ and $y = 2x \\;-\\; 5$. These two lines have the same slope, 2. However they have different y-intercepts.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"869\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/graph-of-two-parallel-lines.png\" alt=\"Graph of two parallel lines\" class=\"wp-image-35805\" title=\"Graph of two parallel lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/graph-of-two-parallel-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/graph-of-two-parallel-lines-214x300.png 214w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-how-to-identify-parallel-lines\">How to Identify Parallel Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand how to find the slope of parallel lines or how to determine whether the given equations of lines represent parallel lines or not.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-using-slope-intercept-form\">Using Slope-Intercept Form<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The slope-intercept form of the equation of a line is given by $y = mx + b$. Write the equations of given lines in the slope-intercept form, compare the equations with $y = mx + b$ to find the value of m (slope). If their slopes are equal, the two equations represent parallel lines.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-using-general-equation\">Using General Equation<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The equations representing parallel lines have equal coefficients for x and y. The line parallel to $ax + by + c_1 = 0$ has the equation of the form $ax + by + c_2 = 0$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-derivation-of-slope-of-parallel-lines\">Derivation of Slope of Parallel Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">If the two lines have slopes of $m_1$ and $m_2$, then the angle between them is given by<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$tan\\theta = \\frac{m_1\\;-\\; m_2}{1 + m_1\\;m_2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The angle formed between two parallel lines is either $0^\\circ$ or $180^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$tan(0^\\circ)$ or $tan(180^\\circ)= \\frac{m_1\\;-\\; m_2}{1 + m_1\\;m_2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 0 = \\frac{m_1\\;-\\;m_2}{1 + m_1\\;m_2}$                             $\\left[ \\therefore tan(0^\\circ) = tan(180^\\circ) = 0\\right]$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 0 = m_1\\;-\\;m_2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow m_1\\;-\\;m_2 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow m_1 = m_2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the slopes of two parallel lines are equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the slope of parallel lines formula is given by $m_1 = m_2$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-equation-of-parallel-lines\">Equation of Parallel Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The line parallel to $ax + by + c_1 = 0$ is $ax + by + c_2 = 0$. Here, we observe that both equations have equal coefficients for x and y. If the equation of a line is given by $y = mx + c$ then the slope of this line is equal to \u201cm.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now let\u2019s understand how to find an equation of a parallel line passing through a point with an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Find the equation of a line passing through the point (2,3) and parallel to the line <\/strong>$2x \u2212 3y + 8 = 0$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The required line is parallel to the line $2x \\;\u2212\\; 3y + 8 = 0$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can rewrite it as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\u22123y = \u22122x \\;\u2212\\; 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = \\frac{2}{3}x + \\frac{8}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The slope of the line $2x \u2212 3y + 8 = 0$ is $m = \\frac{2}{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the slope of the required line is also $\\frac{2}{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The slope-point form of the equation of line is given by $y \\;\u2212\\; y_1 = m (x \\;\u2212\\; x1\u200b)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $(x_1,\\; y_1) = (2,\\; 3)$ and $m = \\frac{2}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y \\;\u2212\\; 3 = \\frac{2}{3} (x \\;\u2212\\; 2\u200b)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3y \\;\u2212\\; 9 = 2x \\;\u2212\\; 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2x \\;\u2212\\; 3y = \\;\u2212\\; 5$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-facts-about-slope-of-parallel-lines\">Facts about Slope of Parallel Lines<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Parallel lines are not always equal in length, but they are always at an equal distance from each other.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Parallel lines do not meet.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A triangle has no parallel line, but opposite sides of the square\/rectangle are parallel, and hence, its slope is the same.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">We can draw an infinite number of lines parallel to a given line.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">All horizontal lines are parallel since the slope of horizontal lines is 0.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Slope of vertical lines is not defined. However, all vertical lines are parallel.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about the slope of parallel lines, how to find the slope of parallel lines, its derivation, and how to find equations of parallel lines. Let\u2019s solve a few examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-solved-examples-on-slope-of-parallel-lines\">Solved Examples on Slope of Parallel Lines<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the slope of a line parallel to <\/strong>$y = 5x + 4$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The equation of the line is $y = 5x + 4$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">On comparing it with $y = mx + c$, we get $m = 5$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Two parallel lines have the same slope.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the slope of the line parallel to $y = 5x + 4$ must be $m = 5$.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>If the slopes of two parallel lines \u201cp\u201d and \u201cq\u201d are <\/strong>$4k \\;\u2212\\; 1$<strong> and <\/strong>$k + 8$<strong> respectively, then find the value of \u201ck.\u201d<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If we have two parallel lines with slopes as $m_1$ and $m_2$, then $m_1 = m_2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 4k\\;-\\;1 = k + 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 4k\\;-\\;k = 8 + 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 3k = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow k = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the value of k is 3.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the slope \u201cm\u201d of the line <\/strong>$y = mx + 5$<strong> if it passes through <\/strong>$(\\;\u2212\\;2,\\; 1)$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The line $y = mx + 5$ passes through $(\\;\u2212\\;2,\\; 1)$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the point $(\\;\u2212\\;2,\\; 1)$ must satisfy the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\therefore 1 = m (\\;\u2212\\;2) + 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 1\\;-\\;5 =\u22122m$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow -\\;4 =\\;\u2212\\;2m$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 4 = 2m$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 2m = 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow m = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The required value of \u201cm\u201d is 2.<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the slope of a line parallel to <\/strong>$3x + 13y + 5 = 0$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given the equation of the line is $3x + 13y + 5 = 0$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To find the slope of the line, let\u2019s express the given equation in $y = mx + c$ form.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3x + 13y + 5 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 13y = \\;-\\;3x + 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow y = \\;-\\;\\frac{3}{13}x + \\frac{5}{13}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $m = \\;-\\;\\frac{3}{13}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As we know, the slope of parallel lines is equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the slope of a line parallel to $3x + 13y + 5 = 0$ is $m =\\;-\\;\\frac{3}{13}$.<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>If a line passes through the points <\/strong>$(\\;\u2212\\;2,\\; \\;\u2212\\;1)$<strong> and <\/strong>$(1,\\; 3)$<strong> and another line has the slope 43. Are both lines parallel?<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given, the first line passes through the points $(\\;\u2212\\;2,\\; \\;\u2212\\;1)$ and $(1,\\;3)$, and another line has the slope $\\frac{4}{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, we will find the slope of the first line using the slope from the two-point formula, which is given by&nbsp; $m_1 = \\frac{y_2\\;-\\;y_1}{x_2\\;-\\;x_1} = \\frac{3\\;-\\;(\\;-\\;1)}{1\\;-\\;(\\;-\\;2)} = \\frac{4}{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Slope of the second line is given as $m_2 = \\frac{4}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since, $m_1 = m_2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, both lines are parallel.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-practice-problems-on-slope-of-parallel-lines\">Practice Problems on Slope of Parallel Lines<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Slope of Parallel Line: Formula, Derivation, Example<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The slopes of two parallel lines are<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">equal<\/div><div class=\"spq_answer_block\" data-value=\"1\">not equal<\/div><div class=\"spq_answer_block\" data-value=\"2\">negative reciprocals<\/div><div class=\"spq_answer_block\" data-value=\"3\">negative<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: equal<br\/>The slopes of two parallel lines are equal.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Two lines with slopes m1 and m2 are parallel if _____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$m_1 = \\;-\\;m_2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$m_1 = m_2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$m_1 \\times m_2 = \\;-\\;1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $m_1 = m_2$<br\/>Two lines with slopes m1 and m2 are parallel if $m_1 = m_2$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the slope of a line that is parallel to a line that has a slope of $\\frac{1}{\\sqrt{3}}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\;-\\; \\frac{1}{\\sqrt{3}}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{\\sqrt{3}}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\sqrt{3}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\;-\\; sqrt{3}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{1}{\\sqrt{3}}$<br\/>Parallel lines have the same slope.<br>\r\nHence, the slope of a line that is parallel to a line that has a slope of $\\frac{1}{\\sqrt{3}}$ is also equal to $\\frac{1}{\\sqrt{3}}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The slope of a line parallel to $y = \\;\u2013\\;x + 4$ is equal to<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$1$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\;-\\;4$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$4$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $-1$<br\/>On comparing $y = \\;\u2013\\;x + 4$ with $y = mx + c$, we get m $= \\;\u2013\\;1$<br>\r\nThe slope of a line parallel to $y = \\;\u2013\\;x + 4$ is also equal to $\u2013\\;1$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The lines $y = 8x + 1$ and $y = \\;\u2013\\;8x + 5$ are<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">parallel<\/div><div class=\"spq_answer_block\" data-value=\"1\">not parallel<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">perpendicular<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: not parallel<br\/>The line $y = 8x + 1$ has the slope 8.<br>\r\nThe line $y = \\;\u2013\\;8x + 5$ has the slope $\\;\u2013\\;8$.<br>\r\nTwo lines with slopes $m_1$ and $m_2$ are parallel if $m_1 = m_2$.<br>\r\nThus, the given lines are not parallel.<\/span><\/div><\/div><\/div><\/div>  <script 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\"What is the slope of a line that is parallel to a line that has a slope of $$\\\\frac{1}{\\\\sqrt{3}}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Parallel lines have the same slope.<br>\r\nHence, the slope of a line that is parallel to a line that has a slope of $$\\\\frac{1}{\\\\sqrt{3}}$$ is also equal to $$\\\\frac{1}{\\\\sqrt{3}}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\; \\\\frac{1}{\\\\sqrt{3}}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Parallel lines have the same slope.<br>\r\nHence, the slope of a line that is parallel to a line that has a slope of $$\\\\frac{1}{\\\\sqrt{3}}$$ is also equal to $$\\\\frac{1}{\\\\sqrt{3}}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\sqrt{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Parallel lines have the same slope.<br>\r\nHence, the slope of a line that is parallel to a line that has a slope of $$\\\\frac{1}{\\\\sqrt{3}}$$ is also equal to $$\\\\frac{1}{\\\\sqrt{3}}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\; sqrt{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Parallel lines have the same slope.<br>\r\nHence, the slope of a line that is parallel to a line that has a slope of $$\\\\frac{1}{\\\\sqrt{3}}$$ is also equal to $$\\\\frac{1}{\\\\sqrt{3}}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{\\\\sqrt{3}}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Parallel lines have the same slope.<br>\r\nHence, the slope of a line that is parallel to a line that has a slope of $$\\\\frac{1}{\\\\sqrt{3}}$$ is also equal to $$\\\\frac{1}{\\\\sqrt{3}}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Parallel lines have the same slope.<br>\r\nHence, the slope of a line that is parallel to a line that has a slope of $$\\\\frac{1}{\\\\sqrt{3}}$$ is also equal to $$\\\\frac{1}{\\\\sqrt{3}}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is equal to\",\n                    \"text\": \"The slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is equal to\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"On comparing $$y = \\\\;\u2013\\\\;x + 4$$ with $$y = mx + c$$, we get m $$= \\\\;\u2013\\\\;1$$<br>\r\nThe slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is also equal to $$\u2013\\\\;1$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On comparing $$y = \\\\;\u2013\\\\;x + 4$$ with $$y = mx + c$$, we get m $$= \\\\;\u2013\\\\;1$$<br>\r\nThe slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is also equal to $$\u2013\\\\;1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On comparing $$y = \\\\;\u2013\\\\;x + 4$$ with $$y = mx + c$$, we get m $$= \\\\;\u2013\\\\;1$$<br>\r\nThe slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is also equal to $$\u2013\\\\;1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On comparing $$y = \\\\;\u2013\\\\;x + 4$$ with $$y = mx + c$$, we get m $$= \\\\;\u2013\\\\;1$$<br>\r\nThe slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is also equal to $$\u2013\\\\;1$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-1$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"On comparing $$y = \\\\;\u2013\\\\;x + 4$$ with $$y = mx + c$$, we get m $$= \\\\;\u2013\\\\;1$$<br>\r\nThe slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is also equal to $$\u2013\\\\;1$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"On comparing $$y = \\\\;\u2013\\\\;x + 4$$ with $$y = mx + c$$, we get m $$= \\\\;\u2013\\\\;1$$<br>\r\nThe slope of a line parallel to $$y = \\\\;\u2013\\\\;x + 4$$ is also equal to $$\u2013\\\\;1$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The lines $$y = 8x + 1$$ and $$y = \\\\;\u2013\\\\;8x + 5$$ are\",\n                    \"text\": \"The lines $$y = 8x + 1$$ and $$y = \\\\;\u2013\\\\;8x + 5$$ are\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The line $$y = 8x + 1$$ has the slope 8.<br>\r\nThe line $$y = \\\\;\u2013\\\\;8x + 5$$ has the slope $$\\\\;\u2013\\\\;8$$.<br>\r\nTwo lines with slopes $$m_1$$ and $$m_2$$ are parallel if $$m_1 = m_2$$.<br>\r\nThus, the given lines are not parallel.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"parallel\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line $$y = 8x + 1$$ has the slope 8.<br>\r\nThe line $$y = \\\\;\u2013\\\\;8x + 5$$ has the slope $$\\\\;\u2013\\\\;8$$.<br>\r\nTwo lines with slopes $$m_1$$ and $$m_2$$ are parallel if $$m_1 = m_2$$.<br>\r\nThus, the given lines are not parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line $$y = 8x + 1$$ has the slope 8.<br>\r\nThe line $$y = \\\\;\u2013\\\\;8x + 5$$ has the slope $$\\\\;\u2013\\\\;8$$.<br>\r\nTwo lines with slopes $$m_1$$ and $$m_2$$ are parallel if $$m_1 = m_2$$.<br>\r\nThus, the given lines are not parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"perpendicular\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The line $$y = 8x + 1$$ has the slope 8.<br>\r\nThe line $$y = \\\\;\u2013\\\\;8x + 5$$ has the slope $$\\\\;\u2013\\\\;8$$.<br>\r\nTwo lines with slopes $$m_1$$ and $$m_2$$ are parallel if $$m_1 = m_2$$.<br>\r\nThus, the given lines are not parallel.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"not parallel\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The line $$y = 8x + 1$$ has the slope 8.<br>\r\nThe line $$y = \\\\;\u2013\\\\;8x + 5$$ has the slope $$\\\\;\u2013\\\\;8$$.<br>\r\nTwo lines with slopes $$m_1$$ and $$m_2$$ are parallel if $$m_1 = m_2$$.<br>\r\nThus, the given lines are not parallel.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The line $$y = 8x + 1$$ has the slope 8.<br>\r\nThe line $$y = \\\\;\u2013\\\\;8x + 5$$ has the slope $$\\\\;\u2013\\\\;8$$.<br>\r\nTwo lines with slopes $$m_1$$ and $$m_2$$ are parallel if $$m_1 = m_2$$.<br>\r\nThus, the given lines are not parallel.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-frequently-asked-questions-on-slope-of-parallel-lines\">Frequently Asked Questions on Slope of Parallel Lines<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\"><strong>How can you prove that two lines are parallel?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\">\n\n<p class=\"eplus-wrapper\">Two lines are parallel if both lines have equal slopes.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\"><strong>What is the condition for three lines to be parallel to each other?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\">\n\n<p class=\"eplus-wrapper\">Let three lines have slopes $m_1,\\; m_2$, and $m_3$. Then the condition for three lines to be parallel to each other is $m_1 = m_2 = m_3$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\"><strong>What is the slope of perpendicular lines?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\">\n\n<p class=\"eplus-wrapper\">Two lines with slopes $m_1$ and $m_2$ are perpendicular if $m_1= \\;-\\;\\frac{1}{m_2}$ .<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\"><strong>What is the formula for the slope of parallel lines?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\">\n\n<p class=\"eplus-wrapper\">If we have two parallel lines with slopes as $m_1$ and $m_2$, then the formula for the slope of parallel lines is $m_1 = m_2$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\"><strong>What is the angle between two parallel lines?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-60edc4e6-88e6-440c-8a24-7ebe50fc9ea7\">\n\n<p class=\"eplus-wrapper\">The angle between two parallel lines is either $0^\\circ$ or $180^\\circ$.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Slope of Parallel Lines? The slope of parallel lines is always equal. Parallel lines have the same slope because their rise over run ratio is equal. They make an equal angle with the positive x-axis. In geometry, parallel lines can be defined as two lines in the same plane that never meet &#8230; <a title=\"Slope of Parallel Line: Formula, Derivation, Example\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/slope-of-parallel-lines\" aria-label=\"More on Slope of Parallel Line: Formula, Derivation, Example\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-28728","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28728","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=28728"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28728\/revisions"}],"predecessor-version":[{"id":35806,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28728\/revisions\/35806"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=28728"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=28728"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=28728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}