document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120587>Question 120587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the slope of any line perpendicular to the line through points (0,5) and <BR>\n" );
document.write( "(-3,-4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88403 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1:  Find the equation of the line through (0,5) and (-3,-4).  Use the two-point form of the line because you are given two points.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=%28%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=%28%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It doesn't matter which point you call 1 and which you call 2 as long as you are consistent.  Let's say (0,5) is point 1, (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "Then the equation for the line becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=%28%28%28-4%29-5%29%2F%28-3-0%29%29%28x-0%29 ALIGN=MIDDLE  ALT=\"y-5=%28%28%28-4%29-5%29%2F%28-3-0%29%29%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And then a little arithmetic to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=%28%28-9%29%2F%28-3%29%29x ALIGN=MIDDLE  ALT=\"y-5=%28%28-9%29%2F%28-3%29%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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;\" >\r<BR>\n" );
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document.write( "And then put the equation into slope-intercept form by solving for y,\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;\" >\r<BR>\n" );
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document.write( "Now, by inspection of the coefficient on the x term, we can see that the slope of the line through the points is 3.\r<BR>\n" );
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document.write( "But we want the slope of a perpendicular line.  The rule is that line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B1%5D ALIGN=MIDDLE  ALT=\"L%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is perpendicular to line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B2%5D ALIGN=MIDDLE  ALT=\"L%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the negative reciprocal of slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=-1%2Fm%5B2%5D ALIGN=MIDDLE  ALT=\"m%5B1%5D=-1%2Fm%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "All we need now is the negative reciprocal of 3, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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