{"id":25325,"date":"2023-04-21T22:21:51","date_gmt":"2023-04-21T21:21:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25325"},"modified":"2023-05-05T15:04:26","modified_gmt":"2023-05-05T14:04:26","slug":"escreve-uma-equacao-da-reta-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25325","title":{"rendered":"Escreve uma equa\u00e7\u00e3o da reta"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25325' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25325' class='GTTabs_curr'><a  id=\"25325_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25325' ><a  id=\"25325_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_25325'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Escreve uma equa\u00e7\u00e3o da reta:<\/p>\n<ol>\n<li>cujo declive \u00e9 3 e que interseta o eixo das ordenadas no ponto \\(\\left( {0, &#8211; 4} \\right)\\).<\/li>\n<li>cujo declive \u00e9 \\( &#8211; \\frac{1}{2}\\) e que passa no ponto \\(\\left( {2, &#8211; 1} \\right)\\).<\/li>\n<li>que passa na origem do referencial e \u00e9 paralela \u00e0 reta de equa\u00e7\u00e3o \\(y = &#8211; 5x + 1\\).<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25325' onClick='GTTabs_show(1,25325)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25325'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Escreve uma equa\u00e7\u00e3o da reta:<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>cujo declive \u00e9 3 e que interseta o eixo das ordenadas no ponto \\(\\left( {0, &#8211; 4} \\right)\\).<\/blockquote>\n<\/li>\n<li>\n<blockquote>cujo declive \u00e9 \\( &#8211; \\frac{1}{2}\\) e que passa no ponto \\(\\left( {2, &#8211; 1} \\right)\\).<\/blockquote>\n<\/li>\n<li>\n<blockquote>que passa na origem do referencial e \u00e9 paralela \u00e0 reta de equa\u00e7\u00e3o \\(y = &#8211; 5x + 1\\).<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>Como o declive da reta \u00e9 3 e a ordenada na origem \u00e9 \\( &#8211; 4\\), ent\u00e3o \\(y = 3x &#8211; 4\\) \u00e9 uma equa\u00e7\u00e3o da reta.<br \/><br \/><\/li>\n<li>Como o declive da reta \u00e9 \\( &#8211; \\frac{1}{2}\\), ent\u00e3o a equa\u00e7\u00e3o \u00e9 da forma \\(y = &#8211; \\frac{1}{2}x + b\\).<br \/>Ora, &#8220;\\(\\left( {2, &#8211; 1} \\right)\\) \u00e9 um ponto dessa reta&#8221;. Logo, \\(\\begin{array}{*{20}{c}}{y\\left( 2 \\right) = &#8211; 1}&amp; \\Leftrightarrow &amp;{ &#8211; \\frac{1}{2} \\times 2 + b = &#8211; 1}&amp; \\Leftrightarrow &amp;{b = 0}\\end{array}\\).<br \/>Ent\u00e3o, \\(y = &#8211; \\frac{1}{2}x\\)\u00a0\u00e9 uma equa\u00e7\u00e3o da reta.<br \/><br \/><\/li>\n<li>Como a reta passa na origem do referencial, ent\u00e3o a ordenada na origem \u00e9 zero.<br \/>Ora, retas paralelas t\u00eam igual declive, logo o declive desta reta \u00e9 \\( &#8211; 5\\).<br \/>Ent\u00e3o, \\(y = &#8211; 5x\\) \u00e9 uma equa\u00e7\u00e3o da reta.<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25334\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25334\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15.png\" data-orig-size=\"939,523\" 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_Pag177-15\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15.png\" class=\"aligncenter wp-image-25334\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15-300x167.png\" alt=\"\" width=\"520\" height=\"290\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15-300x167.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15-768x428.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15.png 939w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/p>\n\n\n\n<p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25325' onClick='GTTabs_show(0,25325)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Escreve uma equa\u00e7\u00e3o da reta: cujo declive \u00e9 3 e que interseta o eixo das ordenadas no ponto \\(\\left( {0, &#8211; 4} \\right)\\). cujo declive \u00e9 \\( &#8211; \\frac{1}{2}\\) e que&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":25335,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,346,345,344,347],"series":[],"class_list":["post-25325","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-grafico","tag-ordenada-na-origem"],"views":60,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag177-15_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25325","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=25325"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25325\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25335"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25325"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25325"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25325"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}