document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=805405>Question 805405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Are the lines parallel, perpendicular, or neither? 3x+4y=12 and 6x+2y=7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #485276 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=485276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Neither.<BR>\n" );
document.write( "If two lines are parallel, they have the same slope.<BR>\n" );
document.write( "If two lines are perpendicular, the product of their slopes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "To find the slope we could solve for y to get the slope intercept form of the equation.<BR>\n" );
document.write( "We do not really need the intercept. We only need the slope, but it's not hard.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=12 ALIGN=MIDDLE  ALT=\"3x%2B4y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-3x%2B12 ALIGN=MIDDLE  ALT=\"4y=-3x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F4%29x%2B12%2F4 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29x%2B12%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y=%28-3%2F4%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B2y=7 ALIGN=MIDDLE  ALT=\"6x%2B2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-6x%2B7 ALIGN=MIDDLE  ALT=\"2y=-6x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-6%2F2%29x%2B7%2F2 ALIGN=MIDDLE  ALT=\"y=%28-6%2F2%29x%2B7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B7%2F2 ALIGN=MIDDLE  ALT=\"y=-3x%2B7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slopes are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "They are not the same number, so the lines are not parallel.<BR>\n" );
document.write( "When you multiply them,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2F4%29%28-3%29=9%2F4 ALIGN=MIDDLE  ALT=\"%28-3%2F4%29%28-3%29=9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "you do not 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;\" >, so the lines are not perpendicular either.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Maybe, to find slopes, you've been told that for a linear equation in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%2BBy=C ALIGN=MIDDLE  ALT=\"Ax%2BBy=C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=12 ALIGN=MIDDLE  ALT=\"3x%2B4y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B2y=7 ALIGN=MIDDLE  ALT=\"6x%2B2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >),<BR>\n" );
document.write( "the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-A%2FB ALIGN=MIDDLE  ALT=\"-A%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "which means take the coefficient of the x, change its sign, and divide it by the coefficient of the y.<BR>\n" );
document.write( "Maybe you are expected memorize formulas and do that.<BR>\n" );
document.write( "With<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=12 ALIGN=MIDDLE  ALT=\"3x%2B4y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you take the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3 ALIGN=MIDDLE  ALT=\"A=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, change it into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-A=-3 ALIGN=MIDDLE  ALT=\"-A=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=4 ALIGN=MIDDLE  ALT=\"B=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B2y=7 ALIGN=MIDDLE  ALT=\"6x%2B2y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >), you take the 6, change it to -6, and divide by 2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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