document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050683>Question 1050683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equations y = 2x - 1 and y = -1/2x + 4 intersect in Quadrant I. Find the area of the triangle formed with this point of intersection and the two y-intercepts of the lines. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #666271 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=666271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the point of intersection<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+2x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-%281%2F2%29%2Ax+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+-%281%2F2%29%2Ax+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+-+1+=+-%281%2F2%29%2Ax+%2B+4+ ALIGN=MIDDLE  ALT=\"+2x+-+1+=+-%281%2F2%29%2Ax+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+-+2+=+-x+%2B+8+ ALIGN=MIDDLE  ALT=\"+4x+-+2+=+-x+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+=+10+ ALIGN=MIDDLE  ALT=\"+5x+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2+ ALIGN=MIDDLE  ALT=\"+x+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+2x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2%2A2+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+2%2A2+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+3+ ALIGN=MIDDLE  ALT=\"+y+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "The intersection is at ( 2,3 )<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Now find the y-intercepts<BR>\n" );
document.write( "by setting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0+ ALIGN=MIDDLE  ALT=\"+x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+2x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2%2A0+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+2%2A0+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-1+ ALIGN=MIDDLE  ALT=\"+y+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( 0, -1 ) <BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-%281%2F2%29%2Ax+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+-%281%2F2%29%2Ax+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-%281%2F2%29%2A0+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+=+-%281%2F2%29%2A0+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4+ ALIGN=MIDDLE  ALT=\"+y+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( 0, 4 }<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "The distance between the 2 y-intercepts is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28+4+-%28-1%29+%29+ ALIGN=MIDDLE  ALT=\"+abs%28+4+-%28-1%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28+5+%29+=+5+ ALIGN=MIDDLE  ALT=\"+abs%28+5+%29+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "The height of the triangle formed is<BR>\n" );
document.write( "the x-value of the intersection ( 2,3 )<BR>\n" );
document.write( "which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+%281%2F2%29%2A5%2A2+ ALIGN=MIDDLE  ALT=\"+A+=+%281%2F2%29%2A5%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+5+ ALIGN=MIDDLE  ALT=\"+A+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The area is 5 square units<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Here's the plot of the lines:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x+-+1%2C+-%281%2F2%29%2Ax+%2B+4+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x+-+1%2C+-%281%2F2%29%2Ax+%2B+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );