document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132228>Question 132228</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321361482/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation of the line passing through (-3, 7) and perpendicular to -7x-8y=77? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96602 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=96602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lines are perpendicular if and only if their slopes are negative reciprocals of each other.  If <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 slope of one of the lines and <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;\" > is the slope of the other line, then they are perpendicular if <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( "Start with the equation of the given line and put it into slope-intercept form (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >) 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=-7x-8y=77 ALIGN=MIDDLE  ALT=\"-7x-8y=77\"   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=-8y=7x%2B77 ALIGN=MIDDLE  ALT=\"-8y=7x%2B77\"   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=-7x%2F8-77%2F8 ALIGN=MIDDLE  ALT=\"y=-7x%2F8-77%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore the slope of the given line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F8 ALIGN=MIDDLE  ALT=\"-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > because that is the coefficient on x when the equation is in slope-intercept form.\r<BR>\n" );
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document.write( "Since you want to derive the equation for a line perpendicular to the given line, you need the negative reciprocal of the slope of the given line, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28-7%2F8%29=8%2F7 ALIGN=MIDDLE  ALT=\"-1%2F%28-7%2F8%29=8%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now that you have the slope determined and you are given a point, you can use the point-slope form to derive the equation of the desired perpendicular.\r<BR>\n" );
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document.write( "Point-slope form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where (<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;\" >) are the co-ordinates of the given point and m is the slope.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=%288%2F7%29%28x-%28-3%29%29 ALIGN=MIDDLE  ALT=\"y-7=%288%2F7%29%28x-%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is an equation for the desired line.  However, you probably want to put it into standard form just like the given equation at the start.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=%288%2F7%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y-7=%288%2F7%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by 7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y-49=8x%2B24 ALIGN=MIDDLE  ALT=\"7y-49=8x%2B24\"   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=-8x%2B7y=24%2B49 ALIGN=MIDDLE  ALT=\"-8x%2B7y=24%2B49\"   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=-8x%2B7y=73 ALIGN=MIDDLE  ALT=\"-8x%2B7y=73\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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