document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=536509>Question 536509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without graphing, determine whether the following pairs of lines are (a)parallel, (b) perpendicular, or (c) neither parallel nor perpendicular.<BR>\n" );
document.write( "     5x-6y=19<BR>\n" );
document.write( "     6x+5y=-30<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352402 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=352402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are they parallel, perpendicular, or neither?<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-6y+=+19 ALIGN=MIDDLE  ALT=\"5x-6y+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5y+=+-30 ALIGN=MIDDLE  ALT=\"6x%2B5y+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First, put both equations 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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-6y+=+19 ALIGN=MIDDLE  ALT=\"5x-6y+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 6y to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+=+6y%2B19 ALIGN=MIDDLE  ALT=\"5x+=+6y%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now subtract 19 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-19+=+6y ALIGN=MIDDLE  ALT=\"5x-19+=+6y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally, divide both sides by 6.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F6%29x-19%2F6+=+y ALIGN=MIDDLE  ALT=\"%285%2F6%29x-19%2F6+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+highlight%28%285%2F6%29%29x-19%2F6 ALIGN=MIDDLE  ALT=\"y+=+highlight%28%285%2F6%29%29x-19%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Similarly for equation 2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B5y+=+-30 ALIGN=MIDDLE  ALT=\"6x%2B5y+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 6x from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+-6x-30 ALIGN=MIDDLE  ALT=\"5y+=+-6x-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide both sides by 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+highlight_green%28%28-6%2F5%29%29x-6 ALIGN=MIDDLE  ALT=\"y+=+highlight_green%28%28-6%2F5%29%29x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Compare with the \"slope-intercept\" form:<BR>\n" );
document.write( "<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 m is the slope.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D+=+5%2F6 ALIGN=MIDDLE  ALT=\"m%5B1%5D+=+5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D+=+%28-6%2F5%29 ALIGN=MIDDLE  ALT=\"m%5B2%5D+=+%28-6%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You'll notice that the slopes are negative reciprocals of each other!<BR>\n" );
document.write( "If two lines are perpendicular, their slopes are the negative reciprocal of each other.<BR>\n" );
document.write( "What's your conclusion?<BR>\n" );
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