document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=749603>Question 749603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the distance from (-6,-3) to the line defined by y=3x+5 . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456095 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A line containing (-6,-3) and is perpendicular to y=3x+5 also contains the point on both lines; this is the point closest to (-6,-3) on y=3x+5.\r<BR>\n" );
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document.write( "You want the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F3%29x%2Bb ALIGN=MIDDLE  ALT=\"y=-%281%2F3%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > which contains (-6,-3).  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%2B%281%2F3%29x ALIGN=MIDDLE  ALT=\"b=y%2B%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b=-3+(1/3)(-6)<BR>\n" );
document.write( "b=-3-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The perpendicular line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F3%29x-5 ALIGN=MIDDLE  ALT=\"y=-%281%2F3%29x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What is the intersection of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F3%29x-5 ALIGN=MIDDLE  ALT=\"y=-%281%2F3%29x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2B5 ALIGN=MIDDLE  ALT=\"y=3x%2B5\"   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=-%281%2F3%29x-5=3x%2B5 ALIGN=MIDDLE  ALT=\"-%281%2F3%29x-5=3x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x-%281%2F3%29x=10 ALIGN=MIDDLE  ALT=\"-3x-%281%2F3%29x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B%281%2F3%29x=-10 ALIGN=MIDDLE  ALT=\"3x%2B%281%2F3%29x=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2B1x=-30 ALIGN=MIDDLE  ALT=\"9x%2B1x=-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x=-30 ALIGN=MIDDLE  ALT=\"10x=-30\"   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 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%28x%29%2B5 ALIGN=MIDDLE  ALT=\"y=3%28x%29%2B5\"   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%28-3%29%2B5 ALIGN=MIDDLE  ALT=\"y=3%28-3%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-9%2B5 ALIGN=MIDDLE  ALT=\"y=-9%2B5\"   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;\" >.\r<BR>\n" );
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document.write( "That is the point (-3,-4).  This is the point on BOTH lines, shortest distance on the y=3x+5 to (-6,-3).\r<BR>\n" );
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document.write( "How far is (-3,-4) from (-6,-3)?\r<BR>\n" );
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document.write( "Distance:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-3-%28-6%29%29%5E2%2B%28-4-%28-3%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-3-%28-6%29%29%5E2%2B%28-4-%28-3%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E2%2B1%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%283%5E2%2B1%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"highlight%28sqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------------this is how far is y=3x+5 to (-6,-3).<BR>\n" );
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