document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158073>Question 158073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this one.<BR>\n" );
document.write( "Determine whether the graphs of the equations are parallel lines, perpendicular lines or niether.<BR>\n" );
document.write( "3x - 8y =  -18<BR>\n" );
document.write( "32x + 12y = -18<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116469 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=116469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help,<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Can someone help me with this one.<BR>\n" );
document.write( "Determine whether the graphs of the equations are parallel lines, perpendicular lines or niether.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+3x+-+8y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32x+%2B+12y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32x+%2B+12y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Thank you!<BR>\n" );
document.write( ".<BR>\n" );
document.write( "First we have to get the two lines in the slope intercept 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;\" > (\"m\" is the slope, \"b\" = y intercept)<BR>\n" );
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document.write( "First equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8y+=+-18+ ALIGN=MIDDLE  ALT=\"+3x+-+8y+=+-18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will move (-8y) to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8y+=+-18+ ALIGN=MIDDLE  ALT=\"+3x+-+8y+=+-18+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8y+%2B+8y+=+-18+%2B+8y+ ALIGN=MIDDLE  ALT=\"+3x+-+8y+%2B+8y+=+-18+%2B+8y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+=+%28-18%29+%2B+8y+ ALIGN=MIDDLE  ALT=\"+3x+=+%28-18%29+%2B+8y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will move (-18) to the left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+=+%28-18%29+%2B+8y+ ALIGN=MIDDLE  ALT=\"+3x+=+%28-18%29+%2B+8y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+18+=+%28-18%29%2B18+%2B+8y+ ALIGN=MIDDLE  ALT=\"+3x+%2B+18+=+%28-18%29%2B18+%2B+8y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+18+=+8y+ ALIGN=MIDDLE  ALT=\"+3x+%2B+18+=+8y+\"   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=+3x+%2B+18+=+8y+ ALIGN=MIDDLE  ALT=\"+3x+%2B+18+=+8y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8y+=+3x+%2B+18++ ALIGN=MIDDLE  ALT=\"+8y+=+3x+%2B+18++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, To get it in slope intercept form, we have to divide each side by \"8\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8y+=+3x+%2B+18++ ALIGN=MIDDLE  ALT=\"+8y+=+3x+%2B+18++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8y%2F8+=+%283x+%2B+18%29%2F8++ ALIGN=MIDDLE  ALT=\"+8y%2F8+=+%283x+%2B+18%29%2F8++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283x+%2B+18%29%2F8++ ALIGN=MIDDLE  ALT=\"+y+=+%283x+%2B+18%29%2F8++\"   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=+y+=+%283x+%2B+18%29%2F8++ ALIGN=MIDDLE  ALT=\"+y+=+%283x+%2B+18%29%2F8++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283%2F8%29x+%2B+18%2F8++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+18%2F8++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283%2F8%29x+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+9%2F4++\"   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=+y+=+%283%2F8%29x+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope intercept equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+3x+-+8y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can check our answer by replacing \"x\" and \"y\" with any point on the line, in both of the different forms of equation<BR>\n" );
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document.write( "We will use the points (-6,0)(x,y) and ( 2, 3)(x,y)( replace \"x\" with (-6), replace \"y\" with \"0\" for our first check, replace \"x\" with \"2\", replace \"y\" with \"3\" in our second check<BR>\n" );
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document.write( "(-6,0), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+3x+-+8y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28-6%29+-+8%280%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+3%28-6%29+-+8%280%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-18%29+-+0+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+%28-18%29+-+0+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-18%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+%28-18%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(-6,0), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283%2F8%29x+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+%283%2F8%29%28-6%29+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+0+=+%283%2F8%29%28-6%29+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+%28-18%2F8%29+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+0+=+%28-18%2F8%29+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+%28-9%2F4%29+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+0+=+%28-9%2F4%29+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Lets check with a different point <BR>\n" );
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document.write( "(2,3) , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+-+8y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+3x+-+8y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%282%29+-+8%283%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+3%282%29+-+8%283%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+-+24+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+6+-+24+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-18%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+%28-18%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >(True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(2,3) , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283%2F8%29x+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+%283%2F8%29%282%29+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+3+=+%283%2F8%29%282%29+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+6%2F8+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+3+=+6%2F8+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+3%2F4+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+3+=+3%2F4+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+12%2F4++ ALIGN=MIDDLE  ALT=\"+3+=+12%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+3+ ALIGN=MIDDLE  ALT=\"+3+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283%2F8%29x+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our first answer<BR>\n" );
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document.write( "Second equation (We are changing equation into slope intercept form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+mx+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+mx+%2B+b+\"   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=+32x+%2B+12y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32x+%2B+12y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We need to move \"32x\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32x+%2B+12y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32x+%2B+12y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32x+-+32x+%2B+12y+=+%28-18%29+-+32x+ ALIGN=MIDDLE  ALT=\"+32x+-+32x+%2B+12y+=+%28-18%29+-+32x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12y+=+%28-18%29+-+32x+ ALIGN=MIDDLE  ALT=\"+12y+=+%28-18%29+-+32x+\"   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=+12y+=+%28-18%29+-+32x+ ALIGN=MIDDLE  ALT=\"+12y+=+%28-18%29+-+32x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12y+=+%28-32x%29+-+18++ ALIGN=MIDDLE  ALT=\"+12y+=+%28-32x%29+-+18++\"   DISABLED_style= \"max-width:90%; height:auto;\" >, To get the equation in slope intercept form, we will divide each side by \"12\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12y+=+%28-32x%29+-+18++ ALIGN=MIDDLE  ALT=\"+12y+=+%28-32x%29+-+18++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12y%2F12+=+%28%28-32x%29+-+18%29%2F12++ ALIGN=MIDDLE  ALT=\"+12y%2F12+=+%28%28-32x%29+-+18%29%2F12++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28%28-32x%29+-+18%29%2F12++ ALIGN=MIDDLE  ALT=\"+y+=+%28%28-32x%29+-+18%29%2F12++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-32%2F12%29x+-+18%2F12++ ALIGN=MIDDLE  ALT=\"+y+=+%28-32%2F12%29x+-+18%2F12++\"   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=+y+=+%28-32%2F12%29x+-+18%2F12++ ALIGN=MIDDLE  ALT=\"+y+=+%28-32%2F12%29x+-+18%2F12++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-8%2F3%29x+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+y+=+%28-8%2F3%29x+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The slope intercept form of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32x+%2B+12y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32x+%2B+12y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-8%2F3%29x+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+y+=+%28-8%2F3%29x+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Lets check using two points again, Lets use (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9%2F16 ALIGN=MIDDLE  ALT=\"+-9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 0)(We will do the first point first)<BR>\n" );
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document.write( "(0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32x+%2B+12y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32x+%2B+12y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32%280%29+%2B+12%28-3%2F2%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32%280%29+%2B+12%28-3%2F2%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+%2B+%28-18%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+0+%2B+%28-18%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-18%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+%28-18%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-8%2F3%29x+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+y+=+%28-8%2F3%29x+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-3%2F2%29+=+%28-8%2F3%29%280%29+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+%28-3%2F2%29+=+%28-8%2F3%29%280%29+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-3%2F2%29+=+0+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+%28-3%2F2%29+=+0+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-3%2F2%29+=+%28-+3%2F2%29++ ALIGN=MIDDLE  ALT=\"+%28-3%2F2%29+=+%28-+3%2F2%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "Second check(second point)<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9%2F16 ALIGN=MIDDLE  ALT=\"+-9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 0) , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32x+%2B+12y+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32x+%2B+12y+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+32%28-9%2F16%29+%2B+12%280%29+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+32%28-9%2F16%29+%2B+12%280%29+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-18%29+%2B+0+=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+%28-18%29+%2B+0+=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-18%29++=+%28-18%29+ ALIGN=MIDDLE  ALT=\"+%28-18%29++=+%28-18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-9%2F16 ALIGN=MIDDLE  ALT=\"+-9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 0), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-8%2F3%29x+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+y+=+%28-8%2F3%29x+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280%29+=+%28-8%2F3%29%28-9%2F16%29+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+%280%29+=+%28-8%2F3%29%28-9%2F16%29+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+72%2F48+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+0+=+72%2F48+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+3%2F2+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+0+=+3%2F2+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-8%2F3%29x+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+y+=+%28-8%2F3%29x+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > is our second answer.<BR>\n" );
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document.write( "Our two equations in slope intercept form are <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283%2F8%29x+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+9%2F4++\"   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=+y+=+%28-8%2F3%29x+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+y+=+%28-8%2F3%29x+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The slope of the first line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F8+ ALIGN=MIDDLE  ALT=\"+3%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the slope of the second line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-8%2F3%29+ ALIGN=MIDDLE  ALT=\"+%28-8%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If two lines are parallel, their slopes would be the same(our lines are not parallel)<BR>\n" );
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document.write( "If two lines are perpendicular, their slopes are the negative reciprocal of each other<BR>\n" );
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document.write( "(examples of negative reciprocals: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-1%2F2%29+ ALIGN=MIDDLE  ALT=\"+%28-1%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-4%2F5%29+ ALIGN=MIDDLE  ALT=\"+%28-4%2F5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F4+ ALIGN=MIDDLE  ALT=\"+5%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-+4%29+ ALIGN=MIDDLE  ALT=\"+%28-+4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+ ALIGN=MIDDLE  ALT=\"+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to find the negative reciprocal of a number, switch the denominator and numerator with each other and add a negative sign)<BR>\n" );
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document.write( "Our two lines are perpendicular, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-8%2F3%29+ ALIGN=MIDDLE  ALT=\"+%28-8%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the negative reciprocal of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F8+ ALIGN=MIDDLE  ALT=\"+3%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( the numbers to the right of the \"x\" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+mx+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+mx+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Our \"b's\" don't have to be the same)<BR>\n" );
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document.write( "Here are the two lines in a graph( lines are in slope-intercept form)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%283%2F8%29x+%2B+9%2F4++ ALIGN=MIDDLE  ALT=\"+y+=+%283%2F8%29x+%2B+9%2F4++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = green line<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-8%2F3%29x+-+3%2F2++ ALIGN=MIDDLE  ALT=\"+y+=+%28-8%2F3%29x+-+3%2F2++\"   DISABLED_style= \"max-width:90%; height:auto;\" > = red line<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing+%28600%2C600%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2C+graph+%28+600%2C+600%2C+-10%2C10%2C-10%2C10%2C%28%28-8%2F3%29x+-+3%2F2%29%2C+%28+%283%2F8%29x+%2B+9%2F4%29+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As you can see the lines are perpendicular<BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );