{"id":6293,"date":"2021-10-12T16:42:28","date_gmt":"2021-10-12T11:12:28","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6293"},"modified":"2021-11-30T16:16:31","modified_gmt":"2021-11-30T10:46:31","slug":"what-is-the-point-slope-form-of-a-line-equation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-point-slope-form-of-a-line-equation\/","title":{"rendered":"What is the Point Slope Form of a Line Equation"},"content":{"rendered":"

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

Let’s begin – <\/p>\n

What is the Point Slope Form of a Line ?<\/h2>\n
\n

The equation of a line which passes through the point \\(P(x_1, y_1)\\) and has the slope ‘m’ is<\/p>\n

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

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

\n

Let \\(Q(x_1, y_1)\\) be the point through which the line passes and let  P(x, y) be any point on the line.<\/p>\n

Then the slope of the line is \\(y – y_1\\over x – x_1\\)<\/p>\n

but, m is the slope of line <\/p>\n

\\(\\therefore\\) m = \\(y – y_1\\over x – x_1\\) \\(\\implies\\) \\(y – y_1\\) = m(\\(x – x_1\\))<\/p>\n

Hence, \\(y – y_1\\) = m\\(x – x_1\\) is the required equation of the line.<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : Find the equation of a line passing through (2, -3) and inclined at an angle of 135 with the positive direction of x-axis.<\/p>\n

Solution<\/span><\/strong> : Here, m = slope of the line = tan 135 = tan(90 + 45) = -cot 45 = -1<\/p>\n

\\(x_1\\) = 2, \\(y_1\\) = -3<\/p>\n

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

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

i.e. y – (-3) = -1(x – 2)<\/p>\n

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

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

Example<\/strong><\/span> : Determine the equation of line through the point (-4, -3) and parallel to x-axis<\/p>\n

Solution<\/span><\/strong> : Here, m = slope of the line = 0,<\/p>\n

\\(x_1\\) = -4, \\(y_1\\) = -3<\/p>\n

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

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

i.e. y + 3 = 0(x + 4)<\/p>\n

\\(\\implies\\) y + 3 = 0.<\/p>\n

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

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

Here you will learn what is the point slope form of a line equation with proof and examples. Let’s begin –  What is the Point Slope Form of a Line ? The equation of a line which passes through the point \\(P(x_1, y_1)\\) and has the slope ‘m’ is \\(y – y_1\\) = m\\((x – …<\/p>\n

What is the Point Slope 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":[628,629],"yoast_head":"\nWhat is the Point Slope Form of a Line Equation - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the point slope 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\/what-is-the-point-slope-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=\"What is the Point Slope Form of a Line Equation - 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