What is the equation of a line perpendicular to y = -3x + 4 that passes through the point (-1, 6)?<\/p>\n\n\n\n
The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To find the equation of a line perpendicular to ( y = -3x + 4 ) that passes through the point ((-1, 6)), we can follow these steps:<\/p>\n\n\n\n The equation ( y = -3x + 4 ) is in slope-intercept form ( y = mx + b ), where ( m ) is the slope. The slope of this line is ( m = -3 ).<\/p>\n\n\n\n Lines that are perpendicular to each other have slopes that are negative reciprocals. To find the negative reciprocal of (-3), we take:<\/p>\n\n\n\n [ We will now use the point-slope form of a linear equation, which is given by:<\/p>\n\n\n\n [ Here, ( m ) is the slope we found, ( \\frac{1}{3} ), and ((x_1, y_1)) is the point ((-1, 6)).<\/p>\n\n\n\n Substituting the values into the point-slope form:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Next, we distribute ( \\frac{1}{3} ) on the right side:<\/p>\n\n\n\n [ Now, add ( 6 ) to both sides to isolate ( y ):<\/p>\n\n\n\n [ Convert ( 6 ) into thirds:<\/p>\n\n\n\n [ So, the equation becomes:<\/p>\n\n\n\n [ Thus, the equation of the line perpendicular to ( y = -3x + 4 ) and passing through the point ((-1, 6)) is:<\/p>\n\n\n\n [ This equation describes a line with a slope of (\\frac{1}{3}), indicating it rises slowly compared to the steep descent of the original line with a slope of (-3).<\/p>\n","protected":false},"excerpt":{"rendered":" What is the equation of a line perpendicular to y = -3x + 4 that passes through the point (-1, 6)? The correct Answer and Explanation is: To find the equation of a line perpendicular to ( y = -3x + 4 ) that passes through the point ((-1, 6)), we can follow these steps: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-147917","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=147917"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147917\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=147917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=147917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=147917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Determine the slope of the given line<\/h3>\n\n\n\n
Step 2: Find the slope of the perpendicular line<\/h3>\n\n\n\n
m_{\\text{perpendicular}} = -\\frac{1}{m} = -\\frac{1}{-3} = \\frac{1}{3}
]<\/p>\n\n\n\nStep 3: Use the point-slope form to find the equation<\/h3>\n\n\n\n
y – y_1 = m(x – x_1)
]<\/p>\n\n\n\n
y – 6 = \\frac{1}{3}(x – (-1))
]<\/p>\n\n\n\n
y – 6 = \\frac{1}{3}(x + 1)
]<\/p>\n\n\n\nStep 4: Rearrange to slope-intercept form<\/h3>\n\n\n\n
y – 6 = \\frac{1}{3}x + \\frac{1}{3}
]<\/p>\n\n\n\n
y = \\frac{1}{3}x + \\frac{1}{3} + 6
]<\/p>\n\n\n\n
6 = \\frac{18}{3}
]<\/p>\n\n\n\n
y = \\frac{1}{3}x + \\frac{1}{3} + \\frac{18}{3} = \\frac{1}{3}x + \\frac{19}{3}
]<\/p>\n\n\n\nFinal Answer<\/h3>\n\n\n\n
\\boxed{y = \\frac{1}{3}x + \\frac{19}{3}}
]<\/p>\n\n\n\n