Use your knowledge of x- and y-intercepts to choose the correct graph of the equation 3x+6y=6.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To find the correct graph of the equation (3x + 6y = 6), we\u2019ll start by determining the x- and y-intercepts. Intercepts are key points where the graph crosses the axes: the x-intercept is where the graph crosses the x-axis (y = 0), and the y-intercept is where the graph crosses the y-axis (x = 0).<\/p>\n\n\n\n Set (y = 0) in the equation and solve for (x):<\/p>\n\n\n\n [ So, the x-intercept is at ((2, 0)).<\/p>\n\n\n\n Set (x = 0) in the equation and solve for (y):<\/p>\n\n\n\n [ So, the y-intercept is at ((0, 1)).<\/p>\n\n\n\n We can also rewrite the equation in slope-intercept form, (y = mx + b), to better understand its graph. Start by isolating (y):<\/p>\n\n\n\n [ This form tells us that the slope (m) is (-\\frac{1}{2}), and the y-intercept (b) is 1. This means that the line has a downward slope, indicating it falls by (\\frac{1}{2}) unit for each 1 unit increase in (x).<\/p>\n\n\n\n To graph this line, plot the intercepts ((2, 0)) and ((0, 1)), then draw a line through these points. The slope of (-\\frac{1}{2}) confirms that the line decreases as (x) increases.<\/p>\n\n\n\n The correct graph of (3x + 6y = 6) is a line passing through ((2, 0)) and ((0, 1)) with a negative slope. These intercepts and the slope match a line with an x-intercept at 2 and a y-intercept at 1, sloping downward from left to right.<\/p>\n","protected":false},"excerpt":{"rendered":" Use your knowledge of x- and y-intercepts to choose the correct graph of the equation 3x+6y=6. The Correct Answer and Explanation is : To find the correct graph of the equation (3x + 6y = 6), we\u2019ll start by determining the x- and y-intercepts. Intercepts are key points where the graph crosses the axes: the […]<\/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-160801","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160801","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=160801"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160801\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Find the X-Intercept<\/h3>\n\n\n\n
3x + 6(0) = 6 \\Rightarrow 3x = 6 \\Rightarrow x = 2
]<\/p>\n\n\n\nStep 2: Find the Y-Intercept<\/h3>\n\n\n\n
3(0) + 6y = 6 \\Rightarrow 6y = 6 \\Rightarrow y = 1
]<\/p>\n\n\n\nStep 3: Rewrite the Equation in Slope-Intercept Form<\/h3>\n\n\n\n
3x + 6y = 6 \\Rightarrow 6y = -3x + 6 \\Rightarrow y = -\\frac{1}{2}x + 1
]<\/p>\n\n\n\nStep 4: Plot the Points and Graph the Line<\/h3>\n\n\n\n
Summary<\/h3>\n\n\n\n