document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=658972>Question 658972</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find an equation for the line perpendicular to the line -4x-8y=3 having the same Y-intercept as 6x-4y=-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410573 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=410573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Since slopes of perpendicular lines are negative reciprocals of each other,\r<BR>\n" );
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document.write( "first find a slope of the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-8y=3 ALIGN=MIDDLE  ALT=\"-4x-8y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope-intercept ALIGN=MIDDLE  ALT=\"slope-intercept\"   DISABLED_style= \"max-width:90%; height:auto;\" > form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-3=8y ALIGN=MIDDLE  ALT=\"-4x-3=8y\"   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=-%284%2F8%29x-3%2F8=y ALIGN=MIDDLE  ALT=\"-%284%2F8%29x-3%2F8=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=y=-%281%2F2%29x-3%2F8 ALIGN=MIDDLE  ALT=\"y=-%281%2F2%29x-3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....as you can see <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-%281%2F2%29 ALIGN=MIDDLE  ALT=\"m=-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3%2F8 ALIGN=MIDDLE  ALT=\"b=-3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now, let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m%5B1%5Dx%2Bb%5B1%5D ALIGN=MIDDLE  ALT=\"y=m%5B1%5Dx%2Bb%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > be a line that is perpendicular on given line\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-%281%2F2%29 ALIGN=MIDDLE  ALT=\"m=-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then negative reciprocals of it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-%281%2F%28-1%2F2%29%29 ALIGN=MIDDLE  ALT=\"m%5B1%5D=-%281%2F%28-1%2F2%29%29\"   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=highlight%28m%5B1%5D=2%29 ALIGN=MIDDLE  ALT=\"highlight%28m%5B1%5D=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " since given that new line has the same <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;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-4y=-6 ALIGN=MIDDLE  ALT=\"6x-4y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D ALIGN=MIDDLE  ALT=\"b%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-4y=-6 ALIGN=MIDDLE  ALT=\"6x-4y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >...first solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"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%2B6=4y ALIGN=MIDDLE  ALT=\"6x%2B6=4y\"   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%2F4%2B6%2F4=y ALIGN=MIDDLE  ALT=\"6x%2F4%2B6%2F4=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=y=%283%2F2%29x%2B3%2F2 ALIGN=MIDDLE  ALT=\"y=%283%2F2%29x%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b%5B1%5D=3%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28b%5B1%5D=3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "now, our line is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=2x%2B3%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=2x%2B3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "let's see our line on a graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now, check if this line is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-3=8y ALIGN=MIDDLE  ALT=\"-4x-3=8y\"   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%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%2C-%281%2F2%29x-3%2F8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%2C-%281%2F2%29x-3%2F8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now check if our line has same <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;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-4y=-6 ALIGN=MIDDLE  ALT=\"6x-4y=-6\"   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%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%2C%283%2F2%29x%2B3%2F2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+2x%2B3%2F2%2C%283%2F2%29x%2B3%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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