document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169128>Question 169128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Indicate if the following set of lines are parallel, perpendicular, neither.<BR>\n" );
document.write( " Show your work\r<BR>\n" );
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document.write( "3x+y=5<BR>\n" );
document.write( "x+y=3\r<BR>\n" );
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document.write( "After finding the slope, and intercept, I think they are parallel. just need verification. <BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124744 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=124744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By=5 ALIGN=MIDDLE  ALT=\"3x%2By=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5-3x ALIGN=MIDDLE  ALT=\"y=5-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B5 ALIGN=MIDDLE  ALT=\"y=-3x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So we can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%2B5 ALIGN=MIDDLE  ALT=\"y=-3x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3 ALIGN=MIDDLE  ALT=\"m=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5 ALIGN=MIDDLE  ALT=\"b=5\"   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%2By=3 ALIGN=MIDDLE  ALT=\"x%2By=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now move onto the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-x ALIGN=MIDDLE  ALT=\"y=3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B3 ALIGN=MIDDLE  ALT=\"y=-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So we can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B3 ALIGN=MIDDLE  ALT=\"y=-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1 ALIGN=MIDDLE  ALT=\"m=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the slope of the first line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3 ALIGN=MIDDLE  ALT=\"m=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the slope of the second line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1 ALIGN=MIDDLE  ALT=\"m=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the two slopes are NOT equal. This means that the two lines are NOT parallel.\r<BR>\n" );
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document.write( "Also, notice that if we multiply the slopes, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%28-1%29=3 ALIGN=MIDDLE  ALT=\"%28-3%29%28-1%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is NOT equal to -1. <BR>\n" );
document.write( "This means that the two slopes are NOT inverse reciprocals of one another. \r<BR>\n" );
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document.write( "So the two lines are NOT perpendicular\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the two lines are neither parallel nor perpendicular.<BR>\n" );
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