document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043689>Question 1043689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the lines 2x-y+3=0 and x-4y-7=0 is farther from origin? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #658842 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the slope of each line.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y%2B3=0 ALIGN=MIDDLE  ALT=\"2x-y%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=2x%2B3 ALIGN=MIDDLE  ALT=\"y%5B1%5D=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=2 ALIGN=MIDDLE  ALT=\"m%5B1%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y-7=0 ALIGN=MIDDLE  ALT=\"x-4y-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=x-7 ALIGN=MIDDLE  ALT=\"4y=x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=x%2F4-7%2F4 ALIGN=MIDDLE  ALT=\"y%5B2%5D=x%2F4-7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=1%2F4 ALIGN=MIDDLE  ALT=\"m%5B2%5D=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The perpendicular line from the origin to each line has a slope that is the negative reciprocal of the given slope.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1p%5D=-1%2F2 ALIGN=MIDDLE  ALT=\"m%5B1p%5D=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2p%5D=-4 ALIGN=MIDDLE  ALT=\"m%5B2p%5D=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then each line goes through the origin so the equation of each line is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0=-1%2F2%28x-0%29 ALIGN=MIDDLE  ALT=\"y-0=-1%2F2%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1p%5D=-%281%2F2%29x ALIGN=MIDDLE  ALT=\"y%5B1p%5D=-%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0=-4%28x-0%29 ALIGN=MIDDLE  ALT=\"y-0=-4%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2p%5D=-4x ALIGN=MIDDLE  ALT=\"y%5B2p%5D=-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the intersection point of each line,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=-%281%2F2%29x ALIGN=MIDDLE  ALT=\"2x%2B3=-%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F2%29x=-3 ALIGN=MIDDLE  ALT=\"%285%2F2%29x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6%2F5 ALIGN=MIDDLE  ALT=\"x=-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F2%29%286%2F5%29 ALIGN=MIDDLE  ALT=\"y=-%281%2F2%29%286%2F5%29\"   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%2F5 ALIGN=MIDDLE  ALT=\"y=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2F5 ALIGN=MIDDLE  ALT=\"-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   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=x%2F4-7%2F4=-4x ALIGN=MIDDLE  ALT=\"x%2F4-7%2F4=-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817%2F4%29x=7%2F4 ALIGN=MIDDLE  ALT=\"%2817%2F4%29x=7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7%2F17 ALIGN=MIDDLE  ALT=\"x=7%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4%287%2F17%29 ALIGN=MIDDLE  ALT=\"y=-4%287%2F17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-28%2F17 ALIGN=MIDDLE  ALT=\"y=-28%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F17 ALIGN=MIDDLE  ALT=\"7%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-28%2F17 ALIGN=MIDDLE  ALT=\"-28%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "So then calculate the distance from the origin to the respective intersection points,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D%5E2=%28-6%2F5-0%29%5E2%2B%283%2F5-0%29%5E2 ALIGN=MIDDLE  ALT=\"D%5B1%5D%5E2=%28-6%2F5-0%29%5E2%2B%283%2F5-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D%5E2=%2836%2F25%29%2B%289%2F25%29 ALIGN=MIDDLE  ALT=\"D%5B1%5D%5E2=%2836%2F25%29%2B%289%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D%5E2=45%2F25 ALIGN=MIDDLE  ALT=\"D%5B1%5D%5E2=45%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D=sqrt%2845%29%2F5 ALIGN=MIDDLE  ALT=\"D%5B1%5D=sqrt%2845%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D=%283%2F5%29sqrt%285%29 ALIGN=MIDDLE  ALT=\"D%5B1%5D=%283%2F5%29sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( ".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D%5E2=%287%2F17-0%29%5E2%2B%28-28%2F17-0%29%5E2 ALIGN=MIDDLE  ALT=\"D%5B2%5D%5E2=%287%2F17-0%29%5E2%2B%28-28%2F17-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D%5E2=%2849%2B784%29%2F17%5E2 ALIGN=MIDDLE  ALT=\"D%5B2%5D%5E2=%2849%2B784%29%2F17%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B2%5D=sqrt%28833%29%2F17 ALIGN=MIDDLE  ALT=\"D%5B2%5D=sqrt%28833%29%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Here's a graphical representation of the problem.<BR>\n" );
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document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=gr2.JPG\">.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );