{"id":6303,"date":"2021-10-12T16:53:39","date_gmt":"2021-10-12T11:23:39","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6303"},"modified":"2021-10-12T22:50:33","modified_gmt":"2021-10-12T17:20:33","slug":"equation-of-line-parallel-to-a-line","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/equation-of-line-parallel-to-a-line\/","title":{"rendered":"Equation of Line Parallel to a Line"},"content":{"rendered":"

Here you will learn what is the equation of line parallel to a given line with examples.<\/p>\n

Let’s begin –<\/p>\n

Equation of Line Parallel to a Line<\/h2>\n
\n

The equation of the line parallel to a given line ax + by + c = 0 is<\/p>\n

ax + by + \\(\\lambda\\),<\/p>\n

where \\(\\lambda\\) is a constant.<\/p>\n<\/blockquote>\n

Proof<\/strong> :<\/p>\n

\n

Let m be the slope of the line ax + by + c = 0, Then,<\/p>\n

m = -\\(a\\over b\\)<\/p>\n

Since the required line is parallel to the given line, the slope of the required line is also m.<\/p>\n

Let \\(c_1\\) be the y-intercept of the required line. Then, its equation is<\/p>\n

y = mx + \\(c_1\\)<\/p>\n

y = -\\(a\\over b\\)x + \\(c_1\\)<\/p>\n

\\(\\implies\\) ax + by – b\\(c_1\\) = 0<\/p>\n

\\(\\implies\\) ax + by + \\(\\lambda\\) = 0, where \\(\\lambda\\) = -b\\(c_1\\) = constant.<\/p>\n<\/blockquote>\n

Note<\/strong> : To write a line parallel to any given line we keep the expression containing x and y same and simply replace the given constant by a new constant \\(\\lambda\\). The value of \\(\\lambda\\) can be determined by some given condition.<\/p>\n

Example<\/strong><\/span> : Find the equation of line which is parallal to the line 3x – 2y + 5 = 0 and passes through the point (5, -6).<\/p>\n

Solution<\/strong><\/span> :  The line parallel to the line 3x – 2y + 5 = 0 is<\/p>\n

3x – 3y + \\(\\lambda\\) = 0                    …………..(i)<\/p>\n

This passes through (5, -6)<\/p>\n

\\(\\therefore\\) 3 \\(\\times\\) 5 – 2 \\(\\times\\) -6 + \\(\\lambda\\) = 0<\/p>\n

\\(\\implies\\) \\(\\lambda\\) = -27.<\/p>\n

Putting \\(\\lambda\\) = -27 in  (i) we get, <\/p>\n

3x – 3y – 27 = 0, which is the required equation of line.<\/p>\n\n\n

\n
Next – Collinearity of Points<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Equation of a Line Perpendicular to a Line<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the equation of line parallel to a given line with examples. Let’s begin – Equation of Line Parallel to a Line The equation of the line parallel to a given line ax + by + c = 0 is ax + by + \\(\\lambda\\), where \\(\\lambda\\) is a constant. …<\/p>\n

Equation of Line Parallel to a Line<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[32],"tags":[],"yoast_head":"\nEquation of Line Parallel to a Line - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the equation of line parallel to a given line with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/equation-of-line-parallel-to-a-line\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equation of Line Parallel to a Line - 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