document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=844453>Question 844453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! I need some help here :). I need to find the equations of lines (i) parallel and (ii) perpendicular to the following and passing through the given point.<BR>\n" );
document.write( "Here is the the equation and given point.<BR>\n" );
document.write( "\"3x - 2y + 4 = 0\" and \"(3,4)\"<BR>\n" );
document.write( "Thanks a bunch! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508776 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=508776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (i)<BR>\n" );
document.write( "If parallel, then the coefficients on x and y are unchanged; but the constant term will be different.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2y%2Bp=0 ALIGN=MIDDLE  ALT=\"3x-2y%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a parallel line for any <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3C%3E4 ALIGN=MIDDLE  ALT=\"p%3C%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Solving for p and then using (3,4),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2y-3x ALIGN=MIDDLE  ALT=\"p=2y-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2%2A4-3%2A3 ALIGN=MIDDLE  ALT=\"p=2%2A4-3%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-1 ALIGN=MIDDLE  ALT=\"p=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The parallel line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283x-2y-1=0%29 ALIGN=MIDDLE  ALT=\"highlight%283x-2y-1=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(ii)<BR>\n" );
document.write( "Sufficient understanding of the standard form of the equation, know that the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then the slope of a line perpendicular to the given line must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F3%29 ALIGN=MIDDLE  ALT=\"-%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The equation we want is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%2Br=0 ALIGN=MIDDLE  ALT=\"2x%2B3y%2Br=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we want to use the given point to solve for r. (One should examine standard form and compare to slope-intercept form to learn how you can use standard form).<BR>\n" );
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document.write( "First solve symbolically for r.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-2x-3y ALIGN=MIDDLE  ALT=\"r=-2x-3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Substitute the point that it should contain.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-2%2A3-3%2A4 ALIGN=MIDDLE  ALT=\"r=-2%2A3-3%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-6-12 ALIGN=MIDDLE  ALT=\"r=-6-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-18 ALIGN=MIDDLE  ALT=\"r=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now knowing r, the equation containing (3,4) and perpendicular to 3x-2y+4=0 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282x%2B3y-18=0%29 ALIGN=MIDDLE  ALT=\"highlight%282x%2B3y-18=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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