{"id":6460,"date":"2011-02-01T00:59:02","date_gmt":"2011-02-01T00:59:02","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6460"},"modified":"2022-01-18T00:45:12","modified_gmt":"2022-01-18T00:45:12","slug":"as-grandezas-x-e-y-sao-directamente-proporcionais","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6460","title":{"rendered":"As grandezas x e y s\u00e3o diretamente proporcionais"},"content":{"rendered":"<p><ul id='GTTabs_ul_6460' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6460' class='GTTabs_curr'><a  id=\"6460_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6460' ><a  id=\"6460_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6460'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sabe-se que as grandezas x e y s\u00e3o diretamente proporcionais:<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6461\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6461\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg\" data-orig-size=\"562,158\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg\" class=\"aligncenter wp-image-6461\" title=\"Tabela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-300x84.jpg\" alt=\"\" width=\"320\" height=\"90\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-300x84.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-150x42.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-400x112.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg 562w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<ol>\n<li>Determina a constante de proporcionalidade.<\/li>\n<li>Completa a tabela.<\/li>\n<li>Completa a express\u00e3o: $y=&#8230;.\\,x$.<\/li>\n<li>Representa graficamente a fun\u00e7\u00e3o.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6460' onClick='GTTabs_show(1,6460)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6460'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6461\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6461\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg\" data-orig-size=\"562,158\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg\" class=\"aligncenter wp-image-6461\" title=\"Tabela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-300x84.jpg\" alt=\"\" width=\"320\" height=\"90\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-300x84.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-150x42.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1-400x112.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-1.jpg 562w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<ol>\n<li>Como as grandezas s\u00e3o diretamente proporcionais, \u00e9 constante a raz\u00e3o entre os valores correspondentes das vari\u00e1veis dependente e independente. Assim, a constante de proporcionalidade \u00e9 $k=\\frac{-8}{2}=-4$.<br \/>\n\u00ad<\/li>\n<li>\u00ad<br \/>\n<table class=\" aligncenter\" style=\"width: 60%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$x$<\/td>\n<td style=\"text-align: center;\">$2$<\/td>\n<td style=\"text-align: center;\">$-\\frac{1}{2}$<\/td>\n<td style=\"text-align: center;\">\u00a0<span style=\"color: #0000ff;\">$3$<\/span><\/td>\n<td style=\"text-align: center;\">$11$<\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$-5$\u00a0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$y$<\/td>\n<td style=\"text-align: center;\">$-8$<\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$2$\u00a0<\/span><\/td>\n<td style=\"text-align: center;\">$-12$<\/td>\n<td style=\"text-align: center;\">\u00a0<span style=\"color: #0000ff;\">$-44$<\/span><\/td>\n<td style=\"text-align: center;\">$20$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>C\u00e1lculos: $-4\\times (-\\frac{1}{2})=2$; $-12\\div (-4)=3$; $-4\\times 11=-44$; $20\\div (-4)=-5$<br \/>\n\u00ad<\/p>\n<\/li>\n<li>\n<p>A express\u00e3o pedida \u00e9 $y=-4x$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>\n<p>Apresenta-se seguidamente uma representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o:<br \/>\n\u00ad<\/p>\n<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":673,\r\n\"height\":431,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 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Completa a tabela. Completa a express\u00e3o: $y=&#8230;.\\,x$. Representa graficamente a fun\u00e7\u00e3o. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20564,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,127],"tags":[128,130],"series":[],"class_list":["post-6460","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-funcoes","tag-funcoes-2","tag-proporcionalidade-directa"],"views":2561,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8V1Pag071-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6460","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6460"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6460\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20564"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6460"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6460"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6460"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6460"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}