{"id":3888,"date":"2021-08-09T21:01:28","date_gmt":"2021-08-09T21:01:28","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3888"},"modified":"2021-11-30T16:37:53","modified_gmt":"2021-11-30T11:07:53","slug":"equation-of-straight-lines","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/equation-of-straight-lines\/","title":{"rendered":"Equation of Straight Lines in all Forms"},"content":{"rendered":"

Here, you will learn equation of straight lines in all forms i.e. slope form, intercept form, normal form and parametric form etc.<\/p>\n

Let’s begin – <\/p>\n

A relation between x and y which is satisfied by co-ordinates of every point lying on a line is called equation of the straight lines. Here, remember that every one degree equation in variable x and y always represent a straight line i.e. ax + by + c = 0 ; a & b \\(\\ne\\) 0 simultaneously.<\/p>\n

\n

(a)  Equation of a line parallel to x-axis at a distance ‘a’ is y = a or y = -a.<\/p>\n

(b)  Equation of x-axis is y = 0<\/p>\n

(c)  Equation of a line parallel to y-axis at a distance ‘b’ is x = b or x = -b.<\/p>\n

(d)  Equation of y-axis is x = 0.<\/p>\n<\/blockquote>\n

Different Equation of Straight Lines <\/h2>\n

(a) Slope Intercept form :<\/strong><\/h4>\n

Let m be the slope of a line and c its intercept on y-axis. Then the equation of this straight line is written as<\/p>\n

\n

y = mx + c.<\/p>\n<\/blockquote>\n

(b) Point Slope form :<\/strong><\/h4>\n

Let m be the slope of a line and it passes through a point (\\(x_1,y_1\\)), then its equation is written as :<\/p>\n

\n

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

(c) Two Point form :<\/strong><\/h4>\n

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

\n

y – \\(y_1\\) = \\(y_2-y_1\\over {x_2-x_1}\\)(x – \\(x_1\\)).<\/p>\n<\/blockquote>\n

(d) Intercept form :<\/strong><\/h4>\n

If a and b are the intercepts made by a line on the axes of x and y, its equation is written as :<\/p>\n

\n

\\(x\\over a\\) + \\(y\\over b\\) = 1<\/p>\n

Length of intercept of line between the coordinate axes = \\(\\sqrt{a^2+b^2}\\)<\/p>\n<\/blockquote>\n

(e) Normal form :<\/strong><\/h4>\n

If p is the length of perpendicular on a line from the origin, and \\(\\alpha\\) the angle which this perpendicular makes with positive x-axis, then the equation of this line is written as<\/p>\n

\n

xcos\\(\\alpha\\) + ysin\\(\\alpha\\) = p (p is always positive)   where 0 \\(\\le\\) \\(\\alpha\\) < 2\\(\\pi\\).<\/p>\n<\/blockquote>\n

(f) Parametric form :<\/strong><\/h4>\n

To find the equation of a straight line which passes through a given point A(h,k) and makes a given angle \\(\\theta\\) with the positive direction of the axis. P(x,y) is any point on the line.<\/p>\n

\n

Let AP = r, then x – h = rcos\\(\\theta\\), y – k = rsin\\(\\theta\\) & \\(x – h\\over {cos\\theta}\\) = \\(y – k\\over {sin\\theta}\\) = r is the equation of straight line.<\/p>\n<\/blockquote>\n

(g) General form :<\/strong><\/h4>\n

We know that a first degree equation in x and y, ax + by + c = 0 always represent a straight line. This form is known as general form of straight line.<\/p>\n

\n

(i)  Slope of this line = -\\(a\\over b\\)<\/p>\n

(ii)  Intercept by this line on x-axis = -\\(c\\over a\\) and Intercept by this line on y-axis = -\\(c\\over b\\)<\/p>\n

(iii)  To change the general form of a line to normal form, first take c to right hand side and make it positive, then divide the whole equation by \\(\\sqrt{a^2+b^2}\\).<\/p>\n<\/blockquote>\n\n\n

Example : <\/span> Equation of a line which passes through point A(2,3) and makes an angle of 45 with x-axis. If this line meet the line x + y + 1 = 0 at a point P then distance AP is-<\/p>\n

Solution : <\/span>Here \\(x_1\\) = 2, \\(y_1\\) = 3 and \\(\\theta\\) = 45

\n Hence \\(x-2\\over cos45\\) = \\(y-3\\over sin45\\) = r

\n from first two parts \\(\\implies\\) x – 2 = y – 3 \\(\\implies\\) x – y + 1 = 0

\n Co-ordinate of point P on this line is (2+\\(r\\over \\sqrt{2}\\), 3+\\(r\\over \\sqrt{2}\\)).

\n If this point is on line x + y + 1 = 0 then

\n (2+\\(r\\over \\sqrt{2}\\)) + (3+\\(r\\over \\sqrt{2}\\)) + 1 = 0     \\(\\implies\\) r = -\\(3\\sqrt{2}\\) ; |r| = \\(3\\sqrt{2}\\)

<\/p>\n\n\n\n

\n
Next – Formula for Angle between Two Lines<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Condition of Concurrency of Lines<\/a><\/div>\n<\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn equation of straight lines in all forms i.e. slope form, intercept form, normal form and parametric form etc. Let’s begin –  A relation between x and y which is satisfied by co-ordinates of every point lying on a line is called equation of the straight lines. Here, remember that every one …<\/p>\n

Equation of Straight Lines in all Forms<\/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":[653,652],"yoast_head":"\nEquation of Straight Lines in all Forms - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn equation of straight lines in all forms i.e. slope form, intercept form, normal form and parametric form etc.\" \/>\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-straight-lines\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equation of Straight Lines in all Forms - 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