document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828236>Question 828236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line parallel to the line x-3y=2 and passing at a distance 2&#8730;10 from the given line. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499167 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=499167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+3y+=+2+ ALIGN=MIDDLE  ALT=\"+x+-+3y+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y+=+x+-+2+ ALIGN=MIDDLE  ALT=\"+3y+=+x+-+2+\"   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%2F3%29%2Ax+-+2%2F3+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F3%29%2Ax+-+2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "The slope of the line I want will<BR>\n" );
document.write( "have a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+m+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > also<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "I need a point that this line will go through<BR>\n" );
document.write( "to get the equation<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Setting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=0+ ALIGN=MIDDLE  ALT=\"+y=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+3%2A0+=+2+ ALIGN=MIDDLE  ALT=\"+x+-+3%2A0+=+2+\"   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( "So, the given line passes through (2,0)<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "The line through this point and perpendicular <BR>\n" );
document.write( "to the given line will have slope = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1%2Fm+=+-3+ ALIGN=MIDDLE  ALT=\"+-1%2Fm+=+-3+\"   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=+%28+y-0+%29+%2F+%28+x-2+%29+=+-3+ ALIGN=MIDDLE  ALT=\"+%28+y-0+%29+%2F+%28+x-2+%29+=+-3+\"   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%2A%28+x-2+%29+ ALIGN=MIDDLE  ALT=\"+y+=+-3%2A%28+x-2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-3x+%2B+6+ ALIGN=MIDDLE  ALT=\"+y+=+-3x+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Now I need to find the point on this line that is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+2%2Asqrt%2810%29+ ALIGN=MIDDLE  ALT=\"+d+=+2%2Asqrt%2810%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > distance from (2,0)<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+2%2Asqrt%2810%29+%29%5E2+=+%28+y-0+%29%5E2+%2B+%28+x-2+%29%5E2+ ALIGN=MIDDLE  ALT=\"+%28+2%2Asqrt%2810%29+%29%5E2+=+%28+y-0+%29%5E2+%2B+%28+x-2+%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=+40+=+y%5E2+%2B+%28x-2%29%5E2+ ALIGN=MIDDLE  ALT=\"+40+=+y%5E2+%2B+%28x-2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting from (1) above:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+=+%28-3x%2B6%29%5E2+%2B+%28x-2%29%5E2+ ALIGN=MIDDLE  ALT=\"+40+=+%28-3x%2B6%29%5E2+%2B+%28x-2%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=+40+=+9x%5E2+-36x+%2B+36+%2B+x%5E2+-+4x+%2B+4+ ALIGN=MIDDLE  ALT=\"+40+=+9x%5E2+-36x+%2B+36+%2B+x%5E2+-+4x+%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=+10x%5E2+-+40x+=+0+ ALIGN=MIDDLE  ALT=\"+10x%5E2+-+40x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+4x+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+4x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2A%28+x-4%29+=+0+ ALIGN=MIDDLE  ALT=\"+x%2A%28+x-4%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Plugging this into (1),<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-3%2A4+%2B+6+ ALIGN=MIDDLE  ALT=\"+y+=+-3%2A4+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-12+%2B+6+ ALIGN=MIDDLE  ALT=\"+y+=+-12+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-6+ ALIGN=MIDDLE  ALT=\"+y+=+-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Now I have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+m+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the point ( 4,-6)<BR>\n" );
document.write( "Using the point-slope formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28y-%28-6%29+%29+%2F+%28+x-4%29+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+%28y-%28-6%29+%29+%2F+%28+x-4%29+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y%2B6+%29+%2F+%28+x-4+%29+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+%28+y%2B6+%29+%2F+%28+x-4+%29+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+%2B+6+=+%281%2F3%29%2A%28x-4%29+ ALIGN=MIDDLE  ALT=\"+y+%2B+6+=+%281%2F3%29%2A%28x-4%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+%2B+6+=+%281%2F3%29%2Ax+-+4%2F3+ ALIGN=MIDDLE  ALT=\"+y+%2B+6+=+%281%2F3%29%2Ax+-+4%2F3+\"   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%2F3%29%2Ax+-+18%2F3+-+4%2F3+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F3%29%2Ax+-+18%2F3+-+4%2F3+\"   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%2F3%29%2Ax+-22%2F3+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F3%29%2Ax+-22%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "Here's plots of the 3 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%281%2F3%29%2Ax-2%2F3%2C-3x%2B6%2C%281%2F3%29%2Ax-22%2F3+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );