document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=408915>Question 408915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.<BR>\n" );
document.write( "y = (-1/3)x – 5<BR>\n" );
document.write( "-18x + 6y = 21 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287982 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=287982\">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=y+=+%28-1%2F3%29x+%96+5 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F3%29x+%96+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >...this is the slope-intercept form and we can say that slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-1%2F3%29%7D%7D+and+y-intercept+is+%7B%7B%7B-5 ALIGN=MIDDLE  ALT=\"m=%28-1%2F3%29%7D%7D+and+y-intercept+is+%7B%7B%7B-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18x+%2B+6y+=+21 ALIGN=MIDDLE  ALT=\"-18x+%2B+6y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >...write this equation in the slope-intercept form too\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y+=18x+%2B+21 ALIGN=MIDDLE  ALT=\"6y+=18x+%2B+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y%2F6+=18x%2F6+%2B+21%2F6 ALIGN=MIDDLE  ALT=\"6y%2F6+=18x%2F6+%2B+21%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=3x+%2B+3.5 ALIGN=MIDDLE  ALT=\"y+=3x+%2B+3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........we can say that slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3%7D%7D+and+y-intercept+is+%7B%7B%7B3.5 ALIGN=MIDDLE  ALT=\"m=3%7D%7D+and+y-intercept+is+%7B%7B%7B3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so the slopes of our lines are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-1%2F3%29%7D%7D+and+%7B%7B%7Bm=3%7D%7D%0D%0A%0D%0AIf+%7B%7B%7B2 ALIGN=MIDDLE  ALT=\"m=%28-1%2F3%29%7D%7D+and+%7B%7B%7Bm=3%7D%7D%0D%0A%0D%0AIf+%7B%7B%7B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > lines are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" > they have the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > slope; evidently, these two lines are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "If they are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=perpendicular ALIGN=MIDDLE  ALT=\"perpendicular\"   DISABLED_style= \"max-width:90%; height:auto;\" >, their slopes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=multiply ALIGN=MIDDLE  ALT=\"multiply\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; \r<BR>\n" );
document.write( "\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1+=+-1%2Fm2 ALIGN=MIDDLE  ALT=\"m1+=+-1%2Fm2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "let's check it:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3+=+-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3+=+-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........they are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=perpendicular ALIGN=MIDDLE  ALT=\"perpendicular\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "let's see their graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B3.5%2C+-0.33x-5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B3.5%2C+-0.33x-5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );