The graph of the inequality x > 4y + 1 is 1 point of the line x = 4y + 1. *
A. above
B. below
C. to the right
D. to the left<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is C. to the right<\/strong>.<\/p>\n\n\n\n To understand this, let’s analyze the inequality ( x > 4y + 1 ) and its corresponding equation ( x = 4y + 1 ).<\/p>\n\n\n\n 1. Graphing the Equation ( x = 4y + 1 ):<\/strong><\/p>\n\n\n\n This equation represents a straight line. To express it in slope-intercept form (( y = mx + b )), solve for ( y ):<\/p>\n\n\n\n [ Here, the slope (( m )) is ( \\frac{1}{4} ), and the y-intercept (( b )) is ( -\\frac{1}{4} ). This means the line crosses the y-axis at ( -\\frac{1}{4} ) and rises ( 1 ) unit for every ( 4 ) units it runs to the right.<\/p>\n\n\n\n 2. Interpreting the Inequality ( x > 4y + 1 ):<\/strong><\/p>\n\n\n\n The inequality ( x > 4y + 1 ) indicates the region where ( x ) is greater than ( 4y + 1 ). Geometrically, this represents the area to the right of the line ( x = 4y + 1 ). To see why, consider any point ( (x, y) ) on the line: it satisfies ( x = 4y + 1 ). If we increase ( x ) while keeping ( y ) constant, the point moves to the right, and ( x ) becomes greater than ( 4y + 1 ). Conversely, decreasing ( x ) moves the point to the left, where ( x < 4y + 1 ).<\/p>\n\n\n\n 3. Visual Confirmation:<\/strong><\/p>\n\n\n\n To visualize this, plot the line ( x = 4y + 1 ). The region representing ( x > 4y + 1 ) lies entirely to the right of this line. Any point in this region will have an ( x )-coordinate greater than ( 4y + 1 ) for its corresponding ( y )-coordinate.<\/p>\n\n\n\n In summary, the inequality ( x > 4y + 1 ) defines the set of points located to the right of the line ( x = 4y + 1 ). Therefore, the correct answer is C. to the right<\/strong>.<\/p>\n\n\n\n For a visual demonstration of graphing a similar equation, you can refer to the following video:<\/p>\n","protected":false},"excerpt":{"rendered":" The graph of the inequality x > 4y + 1 is 1 point of the line x = 4y + 1. *A. aboveB. belowC. to the rightD. to the left The Correct Answer and Explanation is : The correct answer is C. to the right. To understand this, let’s analyze the inequality ( x > […]<\/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-195580","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195580","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=195580"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195580\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195580"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\begin{align} x &= 4y + 1 \\ x – 1 &= 4y \\ y &= \\frac{1}{4}x – \\frac{1}{4} \\end{align<\/em>}
]<\/p>\n\n\n\n