{"id":25337,"date":"2023-04-22T09:00:38","date_gmt":"2023-04-22T08:00:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25337"},"modified":"2023-05-05T15:04:39","modified_gmt":"2023-05-05T14:04:39","slug":"um-grafico-incompleto","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25337","title":{"rendered":"Um gr\u00e1fico incompleto"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25337' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25337' class='GTTabs_curr'><a  id=\"25337_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25337' ><a  id=\"25337_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_25337'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sem completar o gr\u00e1fico seguinte, diz, justificando, se se trata da representa\u00e7\u00e3o de uma fun\u00e7\u00e3o de proporcionalidade direta.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25338\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25338\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png\" data-orig-size=\"525,225\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag177-16\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png\" class=\"aligncenter wp-image-25338\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16-300x129.png\" alt=\"\" width=\"420\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16-300x129.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png 525w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25337' onClick='GTTabs_show(1,25337)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25337'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Sem completar o gr\u00e1fico seguinte, diz, justificando, se se trata da representa\u00e7\u00e3o de uma fun\u00e7\u00e3o de proporcionalidade direta.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25338\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25338\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png\" data-orig-size=\"525,225\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag177-16\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png\" class=\"aligncenter wp-image-25338\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16-300x129.png\" alt=\"\" width=\"420\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16-300x129.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16.png 525w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/p>\n<p><br \/>Se se trata da representa\u00e7\u00e3o de uma fun\u00e7\u00e3o de proporcionalidade direta, ter\u00e1 de corresponder a uma fun\u00e7\u00e3o linear, que \u00e9 da forma \\(y = ax\\).<\/p>\n<p>Ora, o declive da reta que que cont\u00e9m a parte da representa\u00e7\u00e3o gr\u00e1fica \u00e9 \\(a = \\frac{{45 &#8211; 10}}{{60 &#8211; 25}} = \\frac{{35}}{{35}} = 1\\).<\/p>\n<p>Assim, a procurada fun\u00e7\u00e3o linear \u00e9 \\(y = x\\), a qual n\u00e3o se adequa \u00e0 representa\u00e7\u00e3o gr\u00e1fica, pois a imagem de 25 seria 25, e a imagem de 60 seria 60, e n\u00e3o 10 e 40, respetivamente, conforme se verifica no gr\u00e1fico apresentado.<\/p>\n<p>Portanto, n\u00e3o se trata da representa\u00e7\u00e3o de uma fun\u00e7\u00e3o de proporcionalidade direta.<\/p>\n<p>\u00a0<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_graf.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25347\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25347\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_graf.png\" data-orig-size=\"865,495\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag177-16_graf\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_graf.png\" class=\"aligncenter wp-image-25347\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_graf-300x172.png\" alt=\"\" width=\"520\" height=\"298\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_graf-300x172.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_graf-768x439.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_graf.png 865w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<h6>Resolu\u00e7\u00e3o alternativa<\/h6>\n<p>Ora, \\(\\frac{{45}}{{60}} = \\frac{3}{4} = 0,75\\) e \\(\\frac{{10}}{{25}} = \\frac{2}{5} = 0,4\\).<\/p>\n<p>Portanto, n\u00e3o se trata da representa\u00e7\u00e3o de uma fun\u00e7\u00e3o de proporcionalidade direta, pois n\u00e3o \u00e9 constante o quociente entre os valores correspondentes das duas grandezas, visto que \\(\\frac{{45}}{{60}} \\ne \\frac{{10}}{{25}}\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25337' onClick='GTTabs_show(0,25337)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sem completar o gr\u00e1fico seguinte, diz, justificando, se se trata da representa\u00e7\u00e3o de uma fun\u00e7\u00e3o de proporcionalidade direta. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":25339,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,346,345,710,344],"series":[],"class_list":["post-25337","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-graficos-de-funcoes-afins","tag-8-o-ano","tag-declive","tag-funcao-afim","tag-funcao-linear","tag-grafico"],"views":51,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-16_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25337","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=25337"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25337\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25339"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25337"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25337"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25337"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}