document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93007>Question 93007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Are the following line parallel, perpendicular, or neither?<BR>\n" );
document.write( "L1 through (9,2) and (3,-8)<BR>\n" );
document.write( "L2 through (-3,5) and (5, -1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67712 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=67712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First lets find the slope of the given two lines.\r<BR>\n" );
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document.write( "L1 = (9,2) and (3, -8)  The equation of the line with 2 points is given by: \r<BR>\n" );
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document.write( "(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)\r<BR>\n" );
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document.write( "On substituing for these values we find that\r<BR>\n" );
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document.write( "y + 10x - 92 = 0 \r<BR>\n" );
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document.write( "Similarly find the eqn of the line L2, \r<BR>\n" );
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document.write( "8y + 6x - 22 = 0 \r<BR>\n" );
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document.write( "Now writing both of the equation in the standard form or the slope intercept form, we find the slopes.\r<BR>\n" );
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document.write( "First eqn is:  \r<BR>\n" );
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document.write( "y = -10x + 92  ---------------(1)\r<BR>\n" );
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document.write( "Second Eqn is: \r<BR>\n" );
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document.write( "This can be simplified and written as: \r<BR>\n" );
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document.write( "WE shall first find the slopes of both the equations. \r<BR>\n" );
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document.write( "That is slope of Eqn (1) =  -10 \r<BR>\n" );
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document.write( "And the slope of the Eqn (2) =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-3%2F4%29 ALIGN=MIDDLE  ALT=\"+%28-3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Two lines are said to be parallel if their slopes are equal and have different y-intercepts. \r<BR>\n" );
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document.write( "Two lines are said to be perpendicular if the product of their slopes is equals negative one. \r<BR>\n" );
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document.write( "So here in the above example we observe that neither of the above cases hold good for the given two lines.\r<BR>\n" );
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document.write( "Hence, they are neither perpendicular nor parallel. \r<BR>\n" );
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document.write( "The graph of the above 2 equations look in this way. \r<BR>\n" );
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document.write( "Thus the solution\r<BR>\n" );
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document.write( "Regards\r<BR>\n" );
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document.write( " </SPAN>\n" );
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