{"id":25009,"date":"2023-04-13T14:28:18","date_gmt":"2023-04-13T13:28:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=25009"},"modified":"2023-04-18T10:32:03","modified_gmt":"2023-04-18T09:32:03","slug":"determina-as-equacoes-das-retas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=25009","title":{"rendered":"Determina as equa\u00e7\u00f5es das retas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_25009' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_25009' class='GTTabs_curr'><a  id=\"25009_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_25009' ><a  id=\"25009_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_25009'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina as equa\u00e7\u00f5es das seguintes retas.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25010\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25010\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png\" data-orig-size=\"480,557\" 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_Pag165-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png\" class=\"wp-image-25010 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1-259x300.png\" alt=\"\" width=\"300\" height=\"348\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1-259x300.png 259w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png 480w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_25009' onClick='GTTabs_show(1,25009)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_25009'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Determina as equa\u00e7\u00f5es das seguintes retas.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"25010\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=25010\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png\" data-orig-size=\"480,557\" 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_Pag165-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png\" class=\"wp-image-25010 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1-259x300.png\" alt=\"\" width=\"300\" height=\"348\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1-259x300.png 259w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1.png 480w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<p>Vamos determinar a equa\u00e7\u00e3o da reta, <em>r<\/em>, que cont\u00e9m a origem do referencial e o ponto \\(A\\left( {1,\\; &#8211; 2} \\right)\\).<\/p>\n<p>Como a reta \u00e9 n\u00e3o vertical, <em>r<\/em> \u00e9 o gr\u00e1fico de uma fun\u00e7\u00e3o linear.<br \/>Ora, o declive da reta <em>r<\/em> \u00e9 \\(a = f\\left( 1 \\right) = &#8211; 2\\).<br \/>Logo, \\(y = &#8211; 2x\\) \u00e9 a equa\u00e7\u00e3o da reta <em>r<\/em>.<\/p>\n<p>\u00a0<\/p>\n<p>Vamos determinar a equa\u00e7\u00e3o da reta, <em>s<\/em>, que cont\u00e9m a origem do referencial e o ponto \\(B\\left( {2,\\;3} \\right)\\).<\/p>\n<p>Seja \\(a = g\\left( 1 \\right)\\).<br \/>Usando o Teorema de Tales, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{3}{a} = \\frac{2}{1}}&amp; \\Leftrightarrow &amp;{a = \\frac{{3 \\times 1}}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{a = \\frac{3}{2}}\\end{array}\\]<\/p>\n<p>Como a reta \u00e9 n\u00e3o vertical, <em>s<\/em> \u00e9 o gr\u00e1fico de uma fun\u00e7\u00e3o linear.<br \/>Ora, o declive da reta <em>s<\/em> \u00e9 \\(a = g\\left( 1 \\right) = \\frac{3}{2}\\).<br \/>Logo, \\(y = \\frac{3}{2}x\\) \u00e9 a equa\u00e7\u00e3o da reta <em>s<\/em>.<\/p>\n<p>\u00a0<\/p>\n<p>Vamos determinar a equa\u00e7\u00e3o da reta, <em>t<\/em>, que cont\u00e9m a origem do referencial e o ponto \\(C\\left( { &#8211; 1,\\;3} \\right)\\).<\/p>\n<p>Seja \\(a = h\\left( 1 \\right) &lt; 0\\).<br \/>Usando o Teorema de Tales, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{3}{{\\left| a \\right|}} = \\frac{1}{1}}&amp; \\Leftrightarrow &amp;{\\left| a \\right| = \\frac{{3 \\times 1}}{1}}\\\\{}&amp; \\Leftrightarrow &amp;{\\left| a \\right| = 3}\\end{array}\\]<\/p>\n<p>Como a reta \u00e9 n\u00e3o vertical, <em>t<\/em> \u00e9 o gr\u00e1fico de uma fun\u00e7\u00e3o linear.<br \/>Ora, o declive da reta <em>t<\/em> \u00e9 \\(a = h\\left( 1 \\right) = &#8211; 3\\).<br \/>Logo, \\(y = &#8211; 3x\\) \u00e9 a equa\u00e7\u00e3o da reta <em>t<\/em>.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_25009' onClick='GTTabs_show(0,25009)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina as equa\u00e7\u00f5es das seguintes retas. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":25011,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,709],"tags":[424,710,344],"series":[],"class_list":["post-25009","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-funcao-linear","tag-grafico"],"views":135,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/04\/8_Pag165-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25009","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=25009"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/25009\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/25011"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25009"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25009"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25009"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=25009"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}