{"id":6291,"date":"2021-10-12T16:40:26","date_gmt":"2021-10-12T11:10:26","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6291"},"modified":"2021-11-30T16:18:11","modified_gmt":"2021-11-30T10:48:11","slug":"what-is-slope-intercept-form-of-a-line-equation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-slope-intercept-form-of-a-line-equation\/","title":{"rendered":"What is Slope Intercept Form of a Line Equation"},"content":{"rendered":"

Here you will learn what is slope intercept form of a line with examples.<\/p>\n

Let’s begin – <\/p>\n

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

The equation of a line with slope m and making an intercept on y-axis is<\/p>\n

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

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

Let the given line intersects y-axis at Q and makes an angle \\(\\theta\\) with x-axis. \"slopeThen, m = \\(tan\\theta\\).<\/p>\n

Let P(x, y) be any point on the line. Draw PL perpendicular to x-axis and QM \\(\\perp\\) PL.<\/p>\n

Clearly, \\(\\angle\\) MPQ = \\(\\theta\\), QM = OL = x<\/p>\n

and, PM = PL – ML  = PL – OQ = y – c<\/p>\n

From triangle PMQ, we have<\/p>\n

\\(\\tan\\theta\\) = \\(PM\\over QM\\) = \\(y – c\\over x\\)<\/p>\n

\\(\\implies\\) m = \\(y – c\\over x\\)<\/p>\n

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

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

Remark 1<\/strong> : <\/p>\n

\n

If the line passes through the origin, the 0 = m0 + c \\(\\implies\\) c = 0. Therefore, the equation of a line passing through origin is y = mx, where m is the slope of the line.<\/p>\n<\/blockquote>\n

Remark 2<\/strong> : <\/p>\n

\n

If the line is parallel to x-axis, then m = 0, therefore the equation of a line parallel to x-axis is y = c.<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : Find the equation of a line with slope -1 and cutting off an intercept of 4 units on negative direction of y-axis.<\/p>\n

Solution<\/span><\/strong> : Here m = -1 and c = -4<\/p>\n

Substituting these values in y = mx + c, we obtain that the equation of the line is<\/p>\n

y = – x – 4 or, x + y + 4 = 0<\/p>\n

Example<\/strong><\/span> : Find the equation of a straight line which cut off an intercept of 5 units on negative direction of y-axis and makes an angle of 120 with the positive direction of x-axis.<\/p>\n

Solution<\/span><\/strong> : Here m = tan 120 = tan(90 + 30) = -cot 30 = -\\(\\sqrt{3}\\) and c = -5<\/p>\n

Substituting these values in y = mx + c, we obtain that the equation of the line is<\/p>\n

y = – \\(\\sqrt{3}\\)x – 5<\/p>\n

or, \\(\\sqrt{3}\\)x + y + 5 = 0<\/p>\n\n\n

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

Here you will learn what is slope intercept form of a line with examples. Let’s begin –  What is Slope Intercept Form of a Line ? The equation of a line with slope m and making an intercept on y-axis is y = mx + c Proof : Let the given line intersects y-axis at …<\/p>\n

What is Slope Intercept 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":[630,632,631],"yoast_head":"\nWhat is Slope Intercept Form of a Line Equation - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is slope intercept 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-slope-intercept-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 Slope Intercept Form of a Line Equation - 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