document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=672537>Question 672537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the distance between 3x-y+5=0 and 6x-2y-7=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #418190 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=418190\">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=3x-y%2B5=0 ALIGN=MIDDLE  ALT=\"3x-y%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-2y-7=0 ALIGN=MIDDLE  ALT=\"6x-2y-7=0\"   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=3x%2B5=y ALIGN=MIDDLE  ALT=\"3x%2B5=y\"   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=6x-7=2y ALIGN=MIDDLE  ALT=\"6x-7=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-3.5=y ALIGN=MIDDLE  ALT=\"3x-3.5=y\"   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=+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B5%2C+3x-3.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B5%2C+3x-3.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use distance formula and find the distance between one point on \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B5=y ALIGN=MIDDLE  ALT=\"3x%2B5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and one on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-3.5=y ALIGN=MIDDLE  ALT=\"3x-3.5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "easiest way is to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercept ALIGN=MIDDLE  ALT=\"x-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-intercept ALIGN=MIDDLE  ALT=\"y-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "let use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercept ALIGN=MIDDLE  ALT=\"x-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > because lines are parallel and slopes are positive \r<BR>\n" );
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document.write( "and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercepts ALIGN=MIDDLE  ALT=\"x-intercepts\"   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=3x%2B5=y ALIGN=MIDDLE  ALT=\"3x%2B5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >....=>....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B5=0 ALIGN=MIDDLE  ALT=\"3x%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-5 ALIGN=MIDDLE  ALT=\"3x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F3 ALIGN=MIDDLE  ALT=\"x=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.17 ALIGN=MIDDLE  ALT=\"x=-1.17\"   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=x-intercept ALIGN=MIDDLE  ALT=\"x-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F3 ALIGN=MIDDLE  ALT=\"-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   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=3x-3.5=y ALIGN=MIDDLE  ALT=\"3x-3.5=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >....=>....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-3.5=0 ALIGN=MIDDLE  ALT=\"3x-3.5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=3.5 ALIGN=MIDDLE  ALT=\"3x=3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.17 ALIGN=MIDDLE  ALT=\"x=1.17\"   DISABLED_style= \"max-width:90%; height:auto;\" >..=>.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-intercept ALIGN=MIDDLE  ALT=\"x-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.17 ALIGN=MIDDLE  ALT=\"1.17\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "find the distance (note the distance between these two points is equal to the distance between given two lines)\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=hummingbird_distance_2D.solver>Distance between two points in two dimensions</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance (denoted by d) between two points in two dimensions is given by the following formula:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Thus in our case, the required distance is<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%281.17--1.17%29%5E2+%2B+%280-0%29%5E2%29=+2.34+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%281.17--1.17%29%5E2+%2B+%280-0%29%5E2%29=+2.34+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
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document.write( "  For more on this concept, refer to <A  rel=nofollow HREF=Distance_formula.wikipedia>Distance formula</A>.<BR>\n" );
document.write( "  </TD></TR>\n" );
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