{"id":229304,"date":"2025-06-08T05:22:16","date_gmt":"2025-06-08T05:22:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229304"},"modified":"2025-06-08T05:22:18","modified_gmt":"2025-06-08T05:22:18","slug":"parallel-perpendicular-lines-homework-5-linear-equations-slope-intercept-standard-form-directions-determine-if-the-equations-are-parallel-perpendicular-or-neither","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/parallel-perpendicular-lines-homework-5-linear-equations-slope-intercept-standard-form-directions-determine-if-the-equations-are-parallel-perpendicular-or-neither\/","title":{"rendered":"Parallel & Perpendicular Lines Homework 5: Linear Equations Slope-Intercept & Standard Form Directions: Determine if the equations are parallel, perpendicular, or neither"},"content":{"rendered":"\n

Parallel & Perpendicular Lines Homework 5: Linear Equations Slope-Intercept & Standard Form Directions: Determine if the equations are parallel, perpendicular, or neither. 11. y = -3x + 6 and y = 1\/3 x – 8 12. y = 5\/4 x + 1 and y = 5\/4 x – 7 13. 3x + 2y = 6 and y = -3\/2 x + 5 14. 3y = 4x + 15 and 9x + 12y = 12 15. 10x – 2y = 16 and x + 5y = -20 16. 5x + 3y = 3 and 3x + 5y = -25 17. -9y = -3x + 18 and 2x – 6y = 30 18. x – y = 5 and x + y = -10 Given Point Slope: 2 : (-5,1); Slope = 3 Directions: Determine if the equations are parallel, perpendicular, or neither. 11. y = -3x + 6 and y = -8 Neither 12. y = 5\/4 x + 1 and y = 5\/4 x – 7 Parallel 13. 3x + 2y = 6 and y = -3\/2 x + 5 Parallel 14. 3y = 4x + 15 and 9x + 12y = 12 Perpendicular 15. 10x – 2y = 16 and x + 5y = -20 Parallel 16. 5x + 3y = 3 and 3x + 5y = -25 Perpendicular 17. -9y = -3x + 18 and 2x – 6y = 30 Parallel 18. x – y = 5 and x + y = -10 Neither<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Key Concepts<\/strong>:<\/h3>\n\n\n\n
    \n
  1. Parallel lines<\/strong> have equal slopes<\/strong>.<\/li>\n\n\n\n
  2. Perpendicular lines<\/strong> have slopes that are negative reciprocals<\/strong> of each other (e.g., mmm and \u22121\/m-1\/m\u22121\/m).<\/li>\n\n\n\n
  3. If the slopes are neither equal nor negative reciprocals<\/strong>, the lines are neither<\/strong>.<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Problem Analysis<\/strong>:<\/h3>\n\n\n\n

    11.<\/strong> y=\u22123x+6y = -3x + 6y=\u22123x+6 and y=13x\u22128y = \\frac{1}{3}x – 8y=31\u200bx\u22128
    \u2192 Slopes: -3 and 1\/3 \u2192 Negative reciprocals<\/strong> \u2192 Perpendicular<\/strong><\/p>\n\n\n\n

    12.<\/strong> y=54x+1y = \\frac{5}{4}x + 1y=45\u200bx+1 and y=54x\u22127y = \\frac{5}{4}x – 7y=45\u200bx\u22127
    \u2192 Slopes: same (5\/4) \u2192 Parallel<\/strong><\/p>\n\n\n\n

    13.<\/strong> 3x+2y=63x + 2y = 63x+2y=6 \u2192 Solve: y=\u221232x+3y = -\\frac{3}{2}x + 3y=\u221223\u200bx+3
    Compare to: y=\u221232x+5y = -\\frac{3}{2}x + 5y=\u221223\u200bx+5
    \u2192 Same slope: -3\/2 \u2192 Parallel<\/strong><\/p>\n\n\n\n

    14.<\/strong> 3y=4x+153y = 4x + 153y=4x+15 \u2192 y=43x+5y = \\frac{4}{3}x + 5y=34\u200bx+5
    9x+12y=129x + 12y = 129x+12y=12 \u2192 Solve: y=\u221234x+1y = -\\frac{3}{4}x + 1y=\u221243\u200bx+1
    \u2192 Slopes: 4\/3 and -3\/4 \u2192 Negative reciprocals<\/strong> \u2192 Perpendicular<\/strong><\/p>\n\n\n\n

    15.<\/strong> 10x\u22122y=1610x – 2y = 1610x\u22122y=16 \u2192 y=5x\u22128y = 5x – 8y=5x\u22128
    x+5y=\u221220x + 5y = -20x+5y=\u221220 \u2192 y=\u221215x\u22124y = -\\frac{1}{5}x – 4y=\u221251\u200bx\u22124
    \u2192 Slopes: 5 and -1\/5 \u2192 Negative reciprocals<\/strong> \u2192 Perpendicular<\/strong><\/p>\n\n\n\n

    16.<\/strong> 5x+3y=35x + 3y = 35x+3y=3 \u2192 y=\u221253x+1y = -\\frac{5}{3}x + 1y=\u221235\u200bx+1
    3x+5y=\u2212253x + 5y = -253x+5y=\u221225 \u2192 y=\u221235x\u22125y = -\\frac{3}{5}x – 5y=\u221253\u200bx\u22125
    \u2192 Slopes: -5\/3 and -3\/5 \u2192 Not equal or reciprocals \u2192 Neither<\/strong><\/p>\n\n\n\n

    17.<\/strong> \u22129y=\u22123x+18-9y = -3x + 18\u22129y=\u22123x+18 \u2192 y=13x\u22122y = \\frac{1}{3}x – 2y=31\u200bx\u22122
    2x\u22126y=302x – 6y = 302x\u22126y=30 \u2192 y=13x\u22125y = \\frac{1}{3}x – 5y=31\u200bx\u22125
    \u2192 Slopes: both 1\/3 \u2192 Parallel<\/strong><\/p>\n\n\n\n

    18.<\/strong> x\u2212y=5x – y = 5x\u2212y=5 \u2192 y=x\u22125y = x – 5y=x\u22125
    x+y=\u221210x + y = -10x+y=\u221210 \u2192 y=\u2212x\u221210y = -x – 10y=\u2212x\u221210
    \u2192 Slopes: 1 and -1 \u2192 Negative reciprocals<\/strong> \u2192 Perpendicular<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    \u2705 Corrected Answers<\/strong>:<\/h3>\n\n\n\n
    #<\/th>Equations<\/th>Answer<\/th><\/tr><\/thead>
    11<\/td>y=\u22123x+6y = -3x + 6y=\u22123x+6 and y=13x\u22128y = \\frac{1}{3}x – 8y=31\u200bx\u22128<\/td>Perpendicular<\/strong><\/td><\/tr>
    12<\/td>y=54x+1y = \\frac{5}{4}x + 1y=45\u200bx+1 and y=54x\u22127y = \\frac{5}{4}x – 7y=45\u200bx\u22127<\/td>Parallel<\/strong><\/td><\/tr>
    13<\/td>3x+2y=63x + 2y = 63x+2y=6 and y=\u221232x+5y = -\\frac{3}{2}x + 5y=\u221223\u200bx+5<\/td>Parallel<\/strong><\/td><\/tr>
    14<\/td>3y=4x+153y = 4x + 153y=4x+15 and 9x+12y=129x + 12y = 129x+12y=12<\/td>Perpendicular<\/strong><\/td><\/tr>
    15<\/td>10x\u22122y=1610x – 2y = 1610x\u22122y=16 and x+5y=\u221220x + 5y = -20x+5y=\u221220<\/td>Perpendicular<\/strong><\/td><\/tr>
    16<\/td>5x+3y=35x + 3y = 35x+3y=3 and 3x+5y=\u2212253x + 5y = -253x+5y=\u221225<\/td>Neither<\/strong><\/td><\/tr>
    17<\/td>\u22129y=\u22123x+18-9y = -3x + 18\u22129y=\u22123x+18 and 2x\u22126y=302x – 6y = 302x\u22126y=30<\/td>Parallel<\/strong><\/td><\/tr>
    18<\/td>x\u2212y=5x – y = 5x\u2212y=5 and x+y=\u221210x + y = -10x+y=\u221210<\/td>Perpendicular<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
    \n\n\n\n

    \ud83d\udd0d Explanation<\/h3>\n\n\n\n

    To determine if two lines are parallel, perpendicular, or neither, we focus on their slopes<\/strong>. In slope-intercept form y=mx+by = mx + by=mx+b, the coefficient mmm is the slope. Two lines are parallel<\/strong> if they have the same slope<\/strong>, and perpendicular<\/strong> if their slopes are negative reciprocals<\/strong> (e.g., 2 and -1\/2). If the slopes are neither equal nor negative reciprocals, the lines are neither<\/strong>.<\/p>\n\n\n\n

    For example, in #11, the slopes -3 and 1\/3 are negative reciprocals, making the lines perpendicular<\/strong>. In contrast, in #12, both lines have slope 5\/4, so they are parallel<\/strong>. In #13, even though one is in standard form, rewriting it shows it has the same slope as the second equation, thus parallel<\/strong>.<\/p>\n\n\n\n

    In #14, we simplify both equations and find their slopes are 4\/3 and -3\/4 \u2014 negative reciprocals, hence perpendicular<\/strong>. In #15, the slopes 5 and -1\/5 also show a perpendicular<\/strong> relationship. But in #16, after simplifying, we get slopes -5\/3 and -3\/5 \u2014 not reciprocals or equal, so the lines are neither<\/strong>.<\/p>\n\n\n\n

    In #17, both simplified equations have slope 1\/3 \u2192 parallel<\/strong>. Finally, in #18, one slope is 1 and the other -1 \u2014 classic negative reciprocals \u2014 so perpendicular<\/strong>.<\/p>\n\n\n\n

    Understanding these relationships is crucial in geometry and algebra, especially when analyzing graphs, solving systems, or working in coordinate geometry.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Parallel & Perpendicular Lines Homework 5: Linear Equations Slope-Intercept & Standard Form Directions: Determine if the equations are parallel, perpendicular, or neither. 11. y = -3x + 6 and y = 1\/3 x – 8 12. y = 5\/4 x + 1 and y = 5\/4 x – 7 13. 3x + 2y = 6 […]<\/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-229304","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229304","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=229304"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229304\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}