document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154238>Question 154238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A.  Find the equation of the line passing through the points  (3, -5)  and ( 1, -2).\r<BR>\n" );
document.write( "\n" );
document.write( "B. Find the equation of the line perpendicular to the line you found above and passing throught the point ( -1, - 2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113546 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=113546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) The formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+y%5B1%5D%29+%2F+%28x+-+x%5B1%5D%29+=+%28y%5B2%5D+-+y%5B1%5D%29+%2F+%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where<BR>\n" );
document.write( "(3, -5) is (<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;\" >)<BR>\n" );
document.write( "(1, -2) is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Actually, you could interchange (3, -5) and (1, -2) and you'd<BR>\n" );
document.write( "still get the right answer<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+%28-5%29%29+%2F+%28x+-+3%29+=+%28-2+-+%28-5%29%29+%2F+%281+-+3%29 ALIGN=MIDDLE  ALT=\"%28y+-+%28-5%29%29+%2F+%28x+-+3%29+=+%28-2+-+%28-5%29%29+%2F+%281+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+%2B+5%29+%2F+%28x+-+3%29+=+3+%2F+%28-2%29 ALIGN=MIDDLE  ALT=\"%28y+%2B+5%29+%2F+%28x+-+3%29+=+3+%2F+%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%2A%28-2%29 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%2A%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2A%28y+%2B+5%29+=+3%2A%28x+-+3%29 ALIGN=MIDDLE  ALT=\"%28-2%29%2A%28y+%2B+5%29+=+3%2A%28x+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y+-+10+=+3x+-+9 ALIGN=MIDDLE  ALT=\"-2y+-+10+=+3x+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y+=+3x+%2B+1 ALIGN=MIDDLE  ALT=\"-2y+=+3x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%283%2F2%29x+-+1%2F2 ALIGN=MIDDLE  ALT=\"y+=+-%283%2F2%29x+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "Does the line pass through (3, -5) and (1, -2)?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+-%283%2F2%29%2A3+-+1%2F2 ALIGN=MIDDLE  ALT=\"-5+=+-%283%2F2%29%2A3+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+-%289%2F2%29+-+1%2F2 ALIGN=MIDDLE  ALT=\"-5+=+-%289%2F2%29+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+=+-5 ALIGN=MIDDLE  ALT=\"-5+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+-%283%2F2%29%2A1+-+1%2F2 ALIGN=MIDDLE  ALT=\"-2+=+-%283%2F2%29%2A1+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+-2 ALIGN=MIDDLE  ALT=\"-2+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "(b)The slope of the line perpendicular to this<BR>\n" );
document.write( "line must have a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D+=+-%281%2Fm%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m%5B2%5D+=+-%281%2Fm%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D+=+-%283%2F2%29 ALIGN=MIDDLE  ALT=\"m%5B1%5D+=+-%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D+=+2%2F3 ALIGN=MIDDLE  ALT=\"m%5B2%5D+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It passes through (-1 , -2)<BR>\n" );
document.write( "I can use the point-slope formula for this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y+-+y%5B1%5D%29+%2F+%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y+-+y%5B1%5D%29+%2F+%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+=+%28y+-+%28-2%29%29+%2F+%28x+-+%28-1%29%29 ALIGN=MIDDLE  ALT=\"2%2F3+=+%28y+-+%28-2%29%29+%2F+%28x+-+%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3+=+%28y+%2B+2%29+%2F+%28x+%2B+1%29 ALIGN=MIDDLE  ALT=\"2%2F3+=+%28y+%2B+2%29+%2F+%28x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28x+%2B+1%29 ALIGN=MIDDLE  ALT=\"3%2A%28x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28x+%2B+1%29+=+3%2A%28y+%2B+2%29 ALIGN=MIDDLE  ALT=\"2%2A%28x+%2B+1%29+=+3%2A%28y+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2+=+3y+%2B+6 ALIGN=MIDDLE  ALT=\"2x+%2B+2+=+3y+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+2x+-+4 ALIGN=MIDDLE  ALT=\"3y+=+2x+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F3%29x+-+4%2F3 ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x+-+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Does it pass through (-1, -2)?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+%282%2F3%29%2A%28-1%29+-+4%2F3 ALIGN=MIDDLE  ALT=\"-2+=+%282%2F3%29%2A%28-1%29+-+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+-%282%2F3%29+-+4%2F3 ALIGN=MIDDLE  ALT=\"-2+=+-%282%2F3%29+-+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+-2 ALIGN=MIDDLE  ALT=\"-2+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );