{"id":6294,"date":"2021-10-12T16:44:17","date_gmt":"2021-10-12T11:14:17","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6294"},"modified":"2021-11-30T16:04:57","modified_gmt":"2021-11-30T10:34:57","slug":"two-point-form-of-a-line-equation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/two-point-form-of-a-line-equation\/","title":{"rendered":"Two Point Form of a Line Equation"},"content":{"rendered":"

Here you will learn two point form of a line equation with proof and examples.<\/p>\n

Let’s begin –<\/p>\n

Two Point Form of a Line<\/h2>\n
\n

The equation of a line passing through two points \\((x_1, y_1)\\) and \\((x_2, y_2)\\) is <\/p>\n

\\(y – y_1\\) = (\\(y_2 – y_1\\over x_2 – x_1\\))(\\(x_2 – x_1\\))<\/p>\n<\/blockquote>\n

Proof<\/strong> : <\/p>\n

\n

Let m be the slope of line passing through \\((x_1, y_1)\\) and \\((x_2, y_2)\\). Then,<\/p>\n

m = \\(y_2 – y_1\\over x_2 – x_1\\)<\/p>\n

By using point-slope form, the equation of the line is,<\/p>\n

\\(y – y_1\\) = m(\\(x_2 – x_1\\))                       <\/p>\n

\\(y – y_1\\) = (\\(y_2 – y_1\\over x_2 – x_1\\))(\\(x_2 – x_1\\))<\/p>\n

This is the required equation of the line.<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : Find the equation of the line joining the points (-1, 3) and (4, -3).<\/p>\n

Solution<\/span><\/strong> : Here, the two points are \\((x_1, y_1)\\) = (-1, 3) and \\((x_2, y_2)\\) = (4, -2).<\/p>\n

So, the equation of the reuqired line is<\/p>\n

\\(y – y_1\\) = (\\(y_2 – y_1\\over x_2 – x_1\\))(\\(x_2 – x_1\\))<\/p>\n

\\(\\implies\\) y – 3 = \\(3 – (-2)\\over -1 – 4\\)(x + 1)<\/p>\n

\\(\\implies\\) y – 3 = -x – 1 \\(\\implies\\) x + y – 2 = 0.<\/p>\n

Example<\/strong><\/span> : Find the equation of the line joining the points \\((a{t_1}^2, 2at_1)\\) and \\((a{t_2}^2, 2at_2)\\).<\/p>\n

Solution<\/span><\/strong> : Here, the two points are \\((x_1, y_1)\\) = \\((a{t_1}^2, 2at_1)\\) and \\((x_2, y_2)\\) = \\((a{t_2}^2, 2at_2)\\).<\/p>\n

So, the equation of the required line is<\/p>\n

\\(y – y_1\\) = (\\(y_2 – y_1\\over x_2 – x_1\\))(\\(x_2 – x_1\\))<\/p>\n

y – \\(2at_1\\) = \\(2at_2 – 2at_1\\over {at_2}^2 – {at_1}^2\\) \\((x – a{t_1}^2)\\)<\/p>\n

y – \\(2at_1\\) = \\(2\\over t_1 + t_2\\) \\((x – a{t_1}^2)\\)<\/p>\n

\\(\\implies\\) y\\((t_1 + t_2)\\) – \\(2a{t_1}^2\\) – \\(2at_1t_2\\) = 2x – \\(2a{t_1}^2\\)<\/p>\n

\\(\\implies\\) y\\((t_1 + t_2)\\) = 2x + \\(2at_1t_2\\).<\/p>\n\n\n

\n
Next – Intercept Form of a Line Equation<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – What is the Point Slope Form of a Line Equation<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn two point form of a line equation with proof and examples. Let’s begin – Two Point Form of a Line The equation of a line passing through two points \\((x_1, y_1)\\) and \\((x_2, y_2)\\) is  \\(y – y_1\\) = (\\(y_2 – y_1\\over x_2 – x_1\\))(\\(x_2 – x_1\\)) Proof :  Let m …<\/p>\n

Two Point Form of a Line Equation<\/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":[625,627,626],"yoast_head":"\nTwo Point Form of a Line Equation - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn two point form of a line equation with proof and 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\/two-point-form-of-a-line-equation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two Point Form of a Line Equation - 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