{"id":13771,"date":"2020-12-10T07:16:56","date_gmt":"2020-12-10T01:46:56","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=13771"},"modified":"2020-12-10T14:28:19","modified_gmt":"2020-12-10T08:58:19","slug":"point-slope-equation-line","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/point-slope-equation-line\/","title":{"rendered":"Point-Slope Equation of a Line"},"content":{"rendered":"<h2>Point-Slope Equation of a Line<\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/eHPTyYbNmx4?start=220&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h3>Equations of straight line in different forms<\/h3>\n<p><strong>(1) Slope form:<\/strong><br \/>\nEquation of a line through the origin and having slope m is <strong>y = mx<\/strong>.<br \/>\n<strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129355 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-1.jpg\" alt=\"Point-Slope Equation of a Line 1\" width=\"561\" height=\"208\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-1.jpg 561w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-1-300x111.jpg 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/>(2) One point form or Point slope form:<\/strong><br \/>\nEquation of a line through the point (x<sub>1<\/sub>,\u00a0 y<sub>1<\/sub>)\u00a0and having slope m is <strong>y \u2212 y<sub>1 <\/sub>= m(x \u2212 x<sub>1<\/sub>)<\/strong>.<br \/>\n<strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129356 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-2.jpg\" alt=\"Point-Slope Equation of a Line 2\" width=\"412\" height=\"303\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-2.jpg 412w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-2-300x221.jpg 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/>(3) Slope intercept form:<\/strong><br \/>\nEquation of a line (non-vertical) with slope m and cutting off an intercept c on the y-axis is <strong>y = mx + c<\/strong>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129357 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-3.jpg\" alt=\"Point-Slope Equation of a Line 3\" width=\"281\" height=\"219\" \/>The equation of a line with slope m and the x-intercept d is y = m(x \u2212 d).<\/p>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/6w9m9bPKbbQ?start=99&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>(4) Intercept form:<\/strong><br \/>\nIf a straight line cuts x-axis at A and the y-axis at B then OA and OB are known as the intercepts of the line on x-axis and y-axis respectively.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129359 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-4.jpg\" alt=\"Point-Slope Equation of a Line 4\" width=\"276\" height=\"221\" \/>Then, equation of a straight line cutting off intercepts a and b on x\u2013axis and y\u2013axis respectively is \\(\\frac { x }{ a } +\\frac { y }{ b } =1\\).<br \/>\nIf given line is parallel to X axis, then X-intercept is undefined.<br \/>\nIf given line is parallel to Y axis, then Y-intercept is undefined.<\/p>\n<p><strong>(5) Two point form:<\/strong><br \/>\nEquation of the line through the points A(x<sub>1<\/sub>,\u00a0 y<sub>1<\/sub>) and B(x<sub>2<\/sub>, y<sub>2<\/sub>) is, \\((y-{ y }_{ 1 })=\\frac { { y }_{ 2 }-{ y }_{ 1 } }{ { x }_{ 2 }-{ x }_{ 1 } } (x-{ x }_{ 1 })\\).<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129360 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-5.jpg\" alt=\"Point-Slope Equation of a Line 5\" width=\"274\" height=\"242\" \/>In the determinant form it is gives as\u00a0\\(\\left| \\begin{matrix} x &amp; y &amp; 1 \\\\ { x }_{ 1 } &amp; { y }_{ 1 } &amp; 1 \\\\ { x }_{ 2 } &amp; { y }_{ 2 } &amp; 1 \\end{matrix} \\right| =0\\) is the equation of line.<\/p>\n<p><strong>(6) Normal or perpendicular form:<\/strong><br \/>\nThe equation of the straight line upon which the length of the perpendicular from the origin is p and this perpendicular makes an angle \u03b1 with x-axis is x cos \u03b1 + y sin \u03b1 = p.<br \/>\n<strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129361 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-6.jpg\" alt=\"Point-Slope Equation of a Line 6\" width=\"249\" height=\"240\" \/>(7) Symmetrical or parametric or distance form of the line:<\/strong><br \/>\nEquation of a line passing through (x<sub>1<\/sub>,\u00a0 y<sub>1<\/sub>)\u00a0and making an angle \u03b8 with the positive direction of x-axis is ,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129362 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-7.jpg\" alt=\"Point-Slope Equation of a Line 7\" width=\"217\" height=\"64\" \/><br \/>\nwhere r is the distance between the point P(x, y) and A(x<sub>1<\/sub>,\u00a0 y<sub>1<\/sub>).<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-129363 aligncenter\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-8.jpg\" alt=\"Point-Slope Equation of a Line 8\" width=\"301\" height=\"231\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-8.jpg 301w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Point-Slope-Equation-of-a-Line-8-300x230.jpg 300w\" sizes=\"(max-width: 301px) 100vw, 301px\" \/>The co-ordinates of any point on this line may be taken as (x<sub>1<\/sub> \u00b1 r cos \u03b8, y<sub>1<\/sub> \u00b1 r sin \u03b8), known as parametric co-ordinates. \u2018r\u2019 is called the parameter.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Point-Slope Equation of a Line Equations of straight line in different forms (1) Slope form: Equation of a line through the origin and having slope m is y = mx. (2) One point form or Point slope form: Equation of a line through the point (x1,\u00a0 y1)\u00a0and having slope m is y \u2212 y1 = [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[5167,5171,5173,5169,5166,5168,5170,5174,5172],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Point-Slope Equation of a Line - A Plus Topper<\/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:\/\/www.aplustopper.com\/point-slope-equation-line\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Point-Slope Equation of a Line\" \/>\n<meta property=\"og:description\" content=\"Point-Slope Equation of a Line Equations of straight line in different forms (1) Slope form: Equation of a line through the origin and having slope m is y = mx. 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