document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128884>Question 1128884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither.  Show all work and explain your conclusion fully.\r<BR>\n" );
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document.write( "5x+4y=40<BR>\n" );
document.write( "16x=15+20y\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745417 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=745417\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The key to the answer is finding the slope for the lines.<BR>\n" );
document.write( "Solve each equation for y to find the slope-intercept form of each equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B4y=40 ALIGN=MIDDLE  ALT=\"5x%2B4y=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=40-5x ALIGN=MIDDLE  ALT=\"4y=40-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=40%2F4-5x%2F4 ALIGN=MIDDLE  ALT=\"y=40%2F4-5x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F4%29x%2B10 ALIGN=MIDDLE  ALT=\"y=%28-5%2F4%29x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x=15%2B20y ALIGN=MIDDLE  ALT=\"16x=15%2B20y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x-15=20y ALIGN=MIDDLE  ALT=\"16x-15=20y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16x%2F20-15%2F20 ALIGN=MIDDLE  ALT=\"y=16x%2F20-15%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F5%29x-3%2F4 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29x-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "we got different expressions for y, so the lines are not the same line in disguise.<BR>\n" );
document.write( "The slopes (the coefficients of x) are <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Their product is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2F4%29%284%2F5%29=-1 ALIGN=MIDDLE  ALT=\"%28-5%2F4%29%284%2F5%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The fact that the product 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;\" > means that the lines are perpendicular. </SPAN>\n" );
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