document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189774>Question 189774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decide whether the pair of lines is parallel, perpendicular or neither.<BR>\n" );
document.write( "5x+3y=4<BR>\n" );
document.write( "3x-5y=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142708 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=142708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Tahoma\" size=1.5><BR>\n" );
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document.write( "Given Line Eqn <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285x%2B3y=4%28red%28EQN1%29%29%2C3x-5y=3%28red%28EQN2%29%29%29 ALIGN=MIDDLE  ALT=\"system%285x%2B3y=4%28red%28EQN1%29%29%2C3x-5y=3%28red%28EQN2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28EQN1%29 ALIGN=MIDDLE  ALT=\"red%28EQN1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "Let Fy=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3%280%29=4 ALIGN=MIDDLE  ALT=\"5x%2B3%280%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%285%29x%2Fcross%285%29=4%2F5 ALIGN=MIDDLE  ALT=\"cross%285%29x%2Fcross%285%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x=4%2F5%29 ALIGN=MIDDLE  ALT=\"red%28x=4%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x-Intercept (4/5,0)\r<BR>\n" );
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document.write( "Let Fx=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%280%29%2B3y=4 ALIGN=MIDDLE  ALT=\"5%280%29%2B3y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%283%29y%2Fcross%283%29=3%2F4 ALIGN=MIDDLE  ALT=\"cross%283%29y%2Fcross%283%29=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=4%2F3%29 ALIGN=MIDDLE  ALT=\"red%28y=4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y-Intercept (0,4/3)\r<BR>\n" );
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document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28EQN2%29 ALIGN=MIDDLE  ALT=\"red%28EQN2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "Let Fy=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-5%280%29=3 ALIGN=MIDDLE  ALT=\"3x-5%280%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=3x=3 ALIGN=MIDDLE  ALT=\"3x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%283%29x%2Fcross%283%29=cross%283%291%2Fcross%283%291 ALIGN=MIDDLE  ALT=\"cross%283%29x%2Fcross%283%29=cross%283%291%2Fcross%283%291\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x=1%29 ALIGN=MIDDLE  ALT=\"red%28x=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x-Intercept\r<BR>\n" );
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document.write( "Let Fx=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%280%29-5y=3 ALIGN=MIDDLE  ALT=\"3%280%29-5y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5y=3 ALIGN=MIDDLE  ALT=\"-5y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28-5%29y%2Fcross%28-5%29=3%2F-5 ALIGN=MIDDLE  ALT=\"cross%28-5%29y%2Fcross%28-5%29=3%2F-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=-3%2F5%29 ALIGN=MIDDLE  ALT=\"red%28y=-3%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,y-Intercept\r<BR>\n" );
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document.write( "As we see the graph,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-7%2C7%2C-7%2C7%2Cgraph%28400%2C400%2C-7%2C7%2C-7%2C7%2C%284-5x%29%2F3%2C%283x-3%29%2F5%29%2Ccircle%284%2F5%2C0%2C.10%29%2Ccircle%280%2C4%2F3%2C.10%29%2Cblue%28circle%281%2C0%2C.10%29%29%2Cblue%28circle%280%2C-3%2F5%2C.10%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28RED=EQN1%29 ALIGN=MIDDLE  ALT=\"red%28RED=EQN1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28GREEN=EQN2%29 ALIGN=MIDDLE  ALT=\"green%28GREEN=EQN2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To check, we know the Slope of one line is negative reciprocal of the other,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m2=-1%2Fm%5B1%5D ALIGN=MIDDLE  ALT=\"m2=-1%2Fm%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We'll see:\r<BR>\n" );
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document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28EQN1%29 ALIGN=MIDDLE  ALT=\"red%28EQN1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 5x+3y=4 ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-5x%2B4 ALIGN=MIDDLE  ALT=\"3y=-5x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%283%29y%2Fcross%283%29=%28-5x%2B4%29%2F3 ALIGN=MIDDLE  ALT=\"cross%283%29y%2Fcross%283%29=%28-5x%2B4%29%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=highlight%28%28-5%2F3%29%29x%2B%284%2F3%29 ALIGN=MIDDLE  ALT=\"y=highlight%28%28-5%2F3%29%29x%2B%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-5%2F3 ALIGN=MIDDLE  ALT=\"m%5B1%5D=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28EQN2%29 ALIGN=MIDDLE  ALT=\"red%28EQN2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 3x-5y=3 ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=3x-3 ALIGN=MIDDLE  ALT=\"5y=3x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%285%29y%2Fcross%285%29=%283x-3%29%2F5 ALIGN=MIDDLE  ALT=\"cross%285%29y%2Fcross%285%29=%283x-3%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=y=highlight%28%283%2F5%29%29x-3%2F5 ALIGN=MIDDLE  ALT=\"y=highlight%28%283%2F5%29%29x-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=3%2F5 ALIGN=MIDDLE  ALT=\"m%5B2%5D=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Verifying, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=-1%2Fm%5B1%5D ALIGN=MIDDLE  ALT=\"m%5B2%5D=-1%2Fm%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5=-1%2F%28-5%2F3%29=%28-1%29%28-3%2F5%29 ALIGN=MIDDLE  ALT=\"3%2F5=-1%2F%28-5%2F3%29=%28-1%29%28-3%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=3%2F5=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "*The two lines are <font color=blue>perpendicular</font> (Answer)\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Jojo</font>\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );