document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217404>Question 217404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x+2y=3<BR>\n" );
document.write( "2x-4y=6<BR>\n" );
document.write( "are these equations parallel perpendicular or neither? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163940 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x+2y=3<BR>\n" );
document.write( "2x-4y=6\r<BR>\n" );
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document.write( "Are these equations parallel perpendicular or neither?\r<BR>\n" );
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document.write( "Step 1.  Need to put above equation given in standard form to slope-intercept form y=mx+b where m is the slope and b is the y-intecept at x=0 or at point (0,b).  Two lines are parallel when the slopes are equal while two lines are perpendicular when the product of their slopes is equal to 1.\r<BR>\n" );
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document.write( "Step 2. Let's put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2y=3 ALIGN=MIDDLE  ALT=\"4x%2B2y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > in slope-intercept form to find the slope.\r<BR>\n" );
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document.write( "Subtract 4x from both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2y=3 ALIGN=MIDDLE  ALT=\"4x%2B2y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B2y-4x=3-4x ALIGN=MIDDLE  ALT=\"4x%2B2y-4x=3-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=3-4x ALIGN=MIDDLE  ALT=\"2y=3-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide 2 to both sides of equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2F2=3%2F2-4x%2F2 ALIGN=MIDDLE  ALT=\"2y%2F2=3%2F2-4x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B3%2F2 ALIGN=MIDDLE  ALT=\"y=-2x%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the slope m=-2 and the y-intercept b=3/2\r<BR>\n" );
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document.write( "Step 3.  Now, let's put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4y=6 ALIGN=MIDDLE  ALT=\"2x-4y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > in slope-intercept form.\r<BR>\n" );
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document.write( "Add 4y-6 to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4y%2B4y-6=6%2B4y-6 ALIGN=MIDDLE  ALT=\"2x-4y%2B4y-6=6%2B4y-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-6=4y ALIGN=MIDDLE  ALT=\"2x-6=4y\"   DISABLED_style= \"max-width:90%; height:auto;\" >}\r<BR>\n" );
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document.write( "Divide by 4 to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F4-6%2F4=4y%2F4 ALIGN=MIDDLE  ALT=\"2x%2F4-6%2F4=4y%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2-3%2F2=y ALIGN=MIDDLE  ALT=\"x%2F2-3%2F2=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Ax%2F2-3%2F2 ALIGN=MIDDLE  ALT=\"y=1%2Ax%2F2-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the slope m=1/2 and y-intercept b=-3/2}}}\r<BR>\n" );
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document.write( "Step 4.  ANSWER:  Since the product of the slopes found in Steps 2 and 3 is equal to -1, that is, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2A%281%2F2%29=-1 ALIGN=MIDDLE  ALT=\"-2%2A%281%2F2%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > the lines are PERPENDICULAR.\r<BR>\n" );
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document.write( "Here's a graph of the above problem.  Note the slopes and the y-intercepts at x=0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+400%2C400%2C+-10%2C10%2C-10%2C10%2C+-2x%2B3%2F2%2C+x%2F2-3%2F2%29 ALIGN=MIDDLE  ALT=\"graph%28+400%2C400%2C+-10%2C10%2C-10%2C10%2C+-2x%2B3%2F2%2C+x%2F2-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope the above steps were helpful. \r<BR>\n" );
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document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
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