{"id":11596,"date":"2013-02-21T11:23:52","date_gmt":"2013-02-21T11:23:52","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11596"},"modified":"2021-12-26T18:44:11","modified_gmt":"2021-12-26T18:44:11","slug":"reta-a-que-pertencem-os-pontos-dados","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11596","title":{"rendered":"Reta a que pertencem os pontos dados"},"content":{"rendered":"<p><ul id='GTTabs_ul_11596' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11596' class='GTTabs_curr'><a  id=\"11596_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11596' ><a  id=\"11596_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_11596'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Para cada al\u00ednea, represente a reta a que pertencem os pontos dados e defina a fun\u00e7\u00e3o afim cujo gr\u00e1fico \u00e9 a reta que desenhou.<\/p>\n<ol>\n<li>$A\\left( {0, &#8211; 3} \\right)$ e $B\\left( {8,1} \\right)$;<\/li>\n<li>$C\\left( { &#8211; 1,0} \\right)$ e $D\\left( {2,6} \\right)$;<\/li>\n<li>$E\\left( { &#8211; 2,4} \\right)$ e $F\\left( {1, &#8211; 5} \\right)$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11596' onClick='GTTabs_show(1,11596)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11596'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<div style=\"width: 546px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag37-1-V2.png\"><img loading=\"lazy\" decoding=\"async\" class=\" \" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2013\/02\/10-pag37-1-V2.png\" alt=\"Gr\u00e1ficos das fun\u00e7\u00f5es f, g e h\" width=\"536\" height=\"309\" \/><\/a><p class=\"wp-caption-text\">Gr\u00e1ficos das fun\u00e7\u00f5es f, g e h<\/p><\/div>\n<ol>\n<li>O declive da reta AB \u00e9 ${m_{AB}} = \\frac{{ &#8211; 3 &#8211; 1}}{{0 &#8211; 8}} = \\frac{1}{2}$ e a ordenada na origem \u00e9\u00a0$b =\u00a0 &#8211; 3$, pois o ponto $A\\left( {0, &#8211; 3} \\right)$ \u00e9 a interse\u00e7\u00e3o da reta AB com o eixo Oy.\n<p>Logo, $y = \\frac{1}{2}x &#8211; 3$ \u00e9 a equa\u00e7\u00e3o reduzida da reta AB.<\/p>\n<p>Portanto, a fun\u00e7\u00e3o afim cujo gr\u00e1fico \u00e9 a reta AB \u00e9: $$\\begin{array}{*{20}{l}}<br \/>\n{f:}&amp;{\\mathbb{R} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to \\frac{1}{2}x &#8211; 3}<br \/>\n\\end{array}$$<\/p>\n<\/li>\n<li>O declive da reta CD \u00e9 ${m_{CD}} = \\frac{{0 &#8211; 6}}{{ &#8211; 1 &#8211; 2}} = 2$, pelo que a sua equa\u00e7\u00e3o reduzida \u00e9 da forma $y = 2x + b$.\n<p>Como o ponto $C\\left( { &#8211; 1,0} \\right)$ \u00e9 um ponto desta reta, as suas coordenadas t\u00eam de verificar a equa\u00e7\u00e3o anterior: $0 = 2 \\times \\left( { &#8211; 1} \\right) + b \\Leftrightarrow b = 2$. Assim, $y = 2x + 2$ \u00e9 a equa\u00e7\u00e3o reduzida da reta CD.<\/p>\n<p>Portanto, a fun\u00e7\u00e3o afim cujo gr\u00e1fico \u00e9 a reta CD \u00e9: $$\\begin{array}{*{20}{l}}<br \/>\n{g:}&amp;{\\mathbb{R} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to 2x + 2}<br \/>\n\\end{array}$$<\/p>\n<\/li>\n<li>O declive da reta EF \u00e9 ${m_{EF}} = \\frac{{4 + 5}}{{ &#8211; 2 &#8211; 1}} =\u00a0 &#8211; 3$, pelo que a sua equa\u00e7\u00e3o reduzida \u00e9 da forma $y =\u00a0 &#8211; 3x + b$.\n<p>Como o ponto $E\\left( { &#8211; 2,4} \\right)$ \u00e9 um ponto desta reta, as suas coordenadas t\u00eam de verificar a equa\u00e7\u00e3o anterior: $4 =\u00a0 &#8211; 3 \\times \\left( { &#8211; 2} \\right) + b \\Leftrightarrow b =\u00a0 &#8211; 2$. Assim, $y =\u00a0 &#8211; 3x &#8211; 2$ \u00e9 a equa\u00e7\u00e3o reduzida da reta EF.<\/p>\n<p>Portanto, a fun\u00e7\u00e3o afim cujo gr\u00e1fico \u00e9 a reta\u00a0EF \u00e9: $$\\begin{array}{*{20}{l}}<br \/>\n{h:}&amp;{\\mathbb{R} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to\u00a0 &#8211; 3x &#8211; 2}<br \/>\n\\end{array}$$<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11596' onClick='GTTabs_show(0,11596)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Para cada al\u00ednea, represente a reta a que pertencem os pontos dados e defina a fun\u00e7\u00e3o afim cujo gr\u00e1fico \u00e9 a reta que desenhou. $A\\left( {0, &#8211; 3} \\right)$ e $B\\left(&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19341,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,343],"tags":[429,346,345,344,347],"series":[],"class_list":["post-11596","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-funcoes-e-graficos","tag-10-o-ano","tag-declive","tag-funcao-afim","tag-grafico","tag-ordenada-na-origem"],"views":2719,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat124.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11596","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=11596"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11596\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19341"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11596"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11596"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11596"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11596"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}