The lines shown below are parallel. If the green line has a slope of 3, what is the slope of the red line?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n If two lines are parallel, their slopes are equal. In this case, you mentioned that the green line has a slope of 3. Therefore, the slope of the red line must also be 3 since it is parallel to the green line.<\/p>\n\n\n\n To understand this concept better, let’s delve into what slope represents and how it applies to parallel lines.<\/p>\n\n\n\n The slope of a line is a measure of its steepness and is calculated as the “rise over run.” This means that for every unit of vertical change (rise), there is a corresponding unit of horizontal change (run). Mathematically, the slope ( m ) is expressed as:<\/p>\n\n\n\n [ where ( (x_1, y_1) ) and ( (x_2, y_2) ) are two points on the line.<\/p>\n\n\n\n Parallel lines have the same slope but different y-intercepts. This means they will never intersect, regardless of how far they are extended. If one line has a slope of ( m_1 ) and another line has a slope of ( m_2 ), and if ( m_1 = m_2 ), the lines are parallel. This property is crucial in various fields, including geometry, algebra, and real-world applications such as engineering and architecture.<\/p>\n\n\n\n In your case, the green line\u2019s slope being 3 indicates that for every 1 unit you move to the right along the x-axis, you move up 3 units along the y-axis. The red line, being parallel, behaves the same way. Hence, the slope of the red line is also 3. This equivalence in slope ensures that the two lines will maintain a constant distance apart, reflecting the fundamental property of parallelism.<\/p>\n\n\n\n In summary, since the red line is parallel to the green line with a slope of 3, it also shares this slope, confirming that the slope of the red line is indeed 3<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" The lines shown below are parallel. If the green line has a slope of 3, what is the slope of the red line? The Correct Answer and Explanation is: If two lines are parallel, their slopes are equal. In this case, you mentioned that the green line has a slope of 3. Therefore, the slope […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","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-157602","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157602","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=157602"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157602\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157602"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157602"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157602"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Definition of Slope<\/h3>\n\n\n\n
m = \\frac{y_2 – y_1}{x_2 – x_1}
]<\/p>\n\n\n\nCharacteristics of Parallel Lines<\/h3>\n\n\n\n
Application of the Concept<\/h3>\n\n\n\n