175

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>175</B></div> <div> <B>Representación gráfica de una ecuación lineal</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>Procedimiento</B></div> <div> <B>P</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >ara representar gráficamente una ecuación lineal se tiene encuenta que "toda ecuación de primer grado con dos variables representa una línea recta", y se procede de la siguiente manera:</FONT></div> <div> <FONT SIZE="4" COLOR="#FF9900" FACE="Bell MT" ><B>1.  </B></FONT>Se escribe la ecuación en la forma general a<I>x</I>+b<I>y</I>+c=0.</div> <div> <FONT SIZE="4" COLOR="#FF9900" FACE="Bell MT" ><B>2.</B></FONT>  Se hallan los interceptos con los ejes; para lo cual se calcula el valor de <I>y</I> cuando <I>x</I> es 0 (intercepto con el eje<I>y</I>), y se calcula el valor de <I>x</I> para <I>y</I> igual a 0 (intercepto con el eje<I>x</I>)</div> <div> <B>3.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se construye una tabla de valores (opcional) con los datos obtenidos en el paso anterior</FONT></div> <div> <B>4.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se ubican y señalan en el plano cartesiano los puntos cuyas coordenadas hallamos con anterioridad</FONT></div> <div> <B>5.</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >  Se unen mediante una línea recta los puntos señalados en el plano</FONT></div> <div> <B>P</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >ara hallar la intesección, el punto donde se cortan, de dos rectas en el plano cartesiano, se trazan las gráficas de las dos ecuaciones e, interpolando, se obtienen las coordenadas del punto común.  </FONT></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>E</B>jercicio <FONT SIZE="4" COLOR="#CC0033" FACE="Times New Roman" >25</FONT></div> <div>  <iframe width="560" height="315" src="https://www.youtube.com/embed/ZjgJiXCLOgU" frameborder="0" allowfullscreen></iframe>  </div> <div> <B>E</B>jercicio <FONT SIZE="4" COLOR="#CC0033" FACE="Times New Roman" >30</FONT></div> <div>  <iframe width="640" height="360" src="//www.youtube.com/embed/eMcRLiDjXPI" frameborder="0" allowfullscreen></iframe>  </div> <div> <B>R</B><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >epresentar gráficamente las siguientes ecuaciones:</FONT></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="656" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 271 ><NOBR><div> <IMG SRC="608923bd0.gif" border=0 width="291" height="189" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="215" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>x</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> -<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >2</FONT></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 2</div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>y</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> -<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >2</FONT></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 2</div> </tD> </tR> </TABLE></div> <div>  <A NAME="2_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#FFFFFF" FACE="Times New Roman" >2</FONT></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="6088fdd50.gif" border=0 width="253" height="213" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="653" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 266 ><NOBR><div> <IMG SRC="608a23a50.gif" border=0 width="291" height="165" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="162" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>x</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 5</div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>y</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 5</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> </tR> </TABLE></div> <bR> <bR> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="608b0ffb0.gif" border=0 width="271" height="251" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <bR> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="653" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 243 ><NOBR><div> <IMG SRC="608c338d0.gif" border=0 width="307" height="141" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="215" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>x</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> -<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >6</FONT></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> -<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >6</FONT></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> -<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >6</FONT></div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>y</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> ...</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> ...</div> </tD> </tR> </TABLE></div> <bR> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="608d07ec0.gif" border=0 width="263" height="236" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <bR> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="653" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 223 ><NOBR><div> <IMG SRC="608e338d0.gif" border=0 width="307" height="141" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="215" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>x</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> ...</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> ...</div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>y</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 7</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 7</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 7</div> </tD> </tR> </TABLE></div> <bR> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="608f1ad60.gif" border=0 width="282" height="214" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <bR> <div>  <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>17</div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="653" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 317 ><NOBR><div> <IMG SRC="609023df0.gif" border=0 width="291" height="223" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="162" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>x</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> -2</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#FFCCB2 HEIGHT= 20 WIDTH="48"><div> <I><B>y</B></I></div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> -<FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >6</FONT></div> </tD> </tR> </TABLE></div> <bR> </NOBR></tD> <tD VALIGN=TOP WIDTH="321"><div> <IMG SRC="6091b8360.gif" border=0 width="184" height="310" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </tD> </tR> </TABLE></div> <bR> <div> <B>H</B><FONT SIZE="3" COLOR="#000000" FACE="Times New Roman" >allar la intersección de:</FONT></div> <div>  <A NAME="23"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>23</div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="667" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 270 ><NOBR><div> <IMG SRC="609368070.gif" border=0 width="360" height="263" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="609226f00.gif" border=0 width="294" height="240" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 20 WIDTH="659"><div> Interpolando, hallamos que las rectas se intersectan en el punto <FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" >P(5,3)</FONT>.</div> </tD> </tR> </TABLE></div> <bR> <bR> <DIV ALIGN="LEFT"></DIV> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="2fc828280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="76fa28280.gif" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><IMG SRC="2fca28280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> Por: <FONT SIZE="4" COLOR="#FF9900" FACE="Times New Roman" >Juan Carlos </FONT><FONT SIZE="4" COLOR="#0000FF" FACE="Times New Roman" >Beltrán</FONT> <FONT SIZE="4" COLOR="#FF0000" FACE="Times New Roman" >Beltrán </FONT></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <A HREF="http://calculo21.com/" TARGET="_top" TITLE="http://calculo21.com/"><U><B><IMG SRC="76fee5530.gif" border=0 width="741" height="83" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> <div> | <A HREF="https://calculo21.com/tabla-de-contenido/funciones-y-sus-graficas/" TARGET="_top" TITLE="https://calculo21.com/tabla-de-contenido"><U>Funciones</U></A> | <A HREF="https://calculo21.com/tabla-de-contenido/limites-y-continuidad/" TARGET="_top" TITLE="https://calculo21.com/tabla-de-contenido"><U>Límites y continuidad</U></A> | <A HREF="https://calculo21.com/tabla-de-contenido/la-derivada/" TARGET="_top" TITLE="https://calculo21.com/tabla-de-contenido"><U>La derivada</U></A> | <A HREF="https://calculo21.com/aplicaciones-de-la-derivada/" TARGET="_top" TITLE="https://calculo21.com/aplicaciones-de-la"><U>Aplicaciones de la derivada</U></A> |</div> <div> | <A HREF="https://calculo21.com/tabla-de-contenido/la-integral-y-tecnicas-ee-integracion/" TARGET="_top" TITLE="https://calculo21.com/tabla-de-contenido"><U>La integral</U></A> | <A HREF="https://calculo21.com/aplicaciones-de-la-integral/" TARGET="_top" TITLE="https://calculo21.com/aplicaciones-de-la"><U>Aplicaciones de la integral</U></A> |</div> <div> | <A HREF="https://calculo21.com/tabla-de-contenido/sucesiones-y-series/" TARGET="_top" TITLE="https://calculo21.com/tabla-de-contenido"><U>Sucesiones y series infinitas</U></A> |</div> <div> | <A HREF="https://calculo21.com/ecuaciones-parametricas-y-coordenadas-polares/" TARGET="_top" TITLE="https://calculo21.com/ecuaciones-paramet"><U>Cónicas - Polares - Paramétricas</U></A> |</div> <div> | <A HREF="https://calculo21.com/ecuaciones-diferenciales/" TARGET="_top" TITLE="https://calculo21.com/ecuaciones-diferen"><U>Ecuaciones diferenciales</U></A> |</div> <div> | <A HREF="https://calculo21.com/calculo-vectorial/" TARGET="_top" TITLE="https://calculo21.com/calculo-vectorial/"><U>Cálculo vectorial</U></A> | <A HREF="https://calculo21.com/algebra-lineal/" TARGET="_top" TITLE="https://calculo21.com/algebra-lineal/"><U>Álgebra lineal</U></A> |</div> <div> | <A HREF="http://www.algebra.jcbmat.com/index.htm" TARGET="_top" TITLE="http://www.algebra.jcbmat.com/index.htm"><U>Álgebra de Baldor</U></A> | </div> <div> | <A HREF="http://calculo21.blogspot.com/" TARGET="_top" TITLE="http://calculo21.blogspot.com/"><U>Blog Cálculo21</U></A> | <A HREF="http://videomate21.blogspot.com/" TARGET="_top" TITLE="http://videomate21.blogspot.com/"><U>Blog Algebra de Baldor</U></A> | <A HREF="http://equat21z.blogspot.com/" TARGET="_top" TITLE="http://equat21z.blogspot.com/"><U>Blog Ecuaciones diferenciales</U></A> | <A HREF="http://bancomate.blogspot.com.co/" TARGET="_top" TITLE="http://bancomate.blogspot.com.co/"><U>Blog Banco de matemáticas</U></A> |</div> <div> | <A HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U>Canal de YouTube</U></A> |</div> <bR> </td> <td valign="top" rowspan="2" width=105 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <A HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><B><IMG SRC="76f464580.gif" border=0 width="100" height="600" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> <bR> </td> </tr><tr> <td valign="top" height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div>  <form action="http://www.google.com.co" id="cse-search-box" target="_blank"> <div> <input type="hidden" name="cx" value="partner-pub-6266400581769473:6497222116" /> <input type="hidden" name="ie" value="UTF-8" /> <input type="text" name="q" size="64" /> <input type="submit" name="sa" value="Buscar en MatU" /> </div> </form> <script type="text/javascript" src="http://www.google.com.co/coop/cse/brand?form=cse-search-box&lang=es"></script>  </div> </td> </tr></table></body>