document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196468>Question 1196468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find k so that the line through (2, -3) and (k,2) is:<BR>\n" );
document.write( "a. parallel to 3x+4y=8<BR>\n" );
document.write( "b. perpendicular to 2x-3y= -4\r<BR>\n" );
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document.write( "k=? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829305 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "Let's solve the equation for y<BR>\n" );
document.write( "3x+4y = 8<BR>\n" );
document.write( "4y = -3x+8<BR>\n" );
document.write( "y = -3x/4+8/4<BR>\n" );
document.write( "y = (-3/4)x+2\r<BR>\n" );
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document.write( "This equation is in y = mx+b form<BR>\n" );
document.write( "m = -3/4 = slope<BR>\n" );
document.write( "b = 2 = y intercept\r<BR>\n" );
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document.write( "Parallel lines have equal slopes, but different y intercepts. <BR>\n" );
document.write( "The line through (2,-3) and (k,2) will also have a slope of -3/4\r<BR>\n" );
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document.write( "Let's set up the slope expression for the line through those two points<BR>\n" );
document.write( "m = slope<BR>\n" );
document.write( "m = rise/run<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (2-(-3))/(k-2)<BR>\n" );
document.write( "m = (2+3)/(k-2)<BR>\n" );
document.write( "m = 5/(k-2)\r<BR>\n" );
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document.write( "Set this equal to -3/4 and solve for k<BR>\n" );
document.write( "m = 5/(k-2)<BR>\n" );
document.write( "-3/4 = 5/(k-2)<BR>\n" );
document.write( "-3(k-2) = 4*5<BR>\n" );
document.write( "-3k+6 = 20<BR>\n" );
document.write( "-3k = 20-6<BR>\n" );
document.write( "-3k = 14<BR>\n" );
document.write( "k = -14/3\r<BR>\n" );
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document.write( "======================================================================================\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Solve the given equation for y<BR>\n" );
document.write( "2x-3y = -4<BR>\n" );
document.write( "-3y = -2x-4<BR>\n" );
document.write( "y = -2x/(-3)-4/(-3)<BR>\n" );
document.write( "y = (2/3)x + 4/3<BR>\n" );
document.write( "The slope of this equation is 2/3\r<BR>\n" );
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document.write( "Flip the fraction and flip the sign to get -3/2 as the perpendicular slope.<BR>\n" );
document.write( "The original slope 2/3 and perpendicular slope -3/2 multiply to -1.\r<BR>\n" );
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document.write( "We'll plug -3/2 into the slope formula we set up in part (a) earlier.\r<BR>\n" );
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document.write( "m = 5/(k-2)<BR>\n" );
document.write( "-3/2 = 5/(k-2)<BR>\n" );
document.write( "-3(k-2) = 2*5<BR>\n" );
document.write( "-3k+6 = 10<BR>\n" );
document.write( "-3k = 10-6<BR>\n" );
document.write( "-3k = 4<BR>\n" );
document.write( "k = -4/3<BR>\n" );
document.write( "</font> </SPAN>\n" );
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