document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200253>Question 1200253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of K so that the two lines are perpendicular. Line one contains the points (-6,4) and (-2,5) and line two contains the points (-3,4) and (0,k).\r<BR>\n" );
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document.write( "I know I need to do y2-y1/x2-x1 so I did that for both of them and got (1/4) for the first line and (k-4/3) for the second line. \r<BR>\n" );
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document.write( "Here is where I need help because I don't know what to do next. Any and all help is greatly appreciated :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834338 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=834338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Rule: Any two perpendicular lines, where neither is vertical nor horizontal, will have their slopes multiply to -1.\r<BR>\n" );
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document.write( "The slope through (-6,4) and (-2,5) is 1/4, which you correctly calculated.\r<BR>\n" );
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document.write( "The slope through (-3,4) and (0,k) is (k-4)/3, which you correctly calculated.\r<BR>\n" );
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document.write( "Multiply those slopes and set the product equal to -1.<BR>\n" );
document.write( "slope1*slope2 = -1<BR>\n" );
document.write( "(1/4)*(k-4)/3 = -1<BR>\n" );
document.write( "(k-4)/12 = -1<BR>\n" );
document.write( "k-4 = -1*12<BR>\n" );
document.write( "k-4 = -12<BR>\n" );
document.write( "k = -12+4<BR>\n" );
document.write( "k = <font color=red size=4>-8</font> is the final answer.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Compute the slope of the line through (-3,4) and (0,-8)<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (-8-4)/(0-(-3))<BR>\n" );
document.write( "m = (-8-4)/(0+3)<BR>\n" );
document.write( "m = -12/3<BR>\n" );
document.write( "m = -4<BR>\n" );
document.write( "This slope of -4 must multiply with the other slope of 1/4 to get a product of -1.<BR>\n" );
document.write( "Sure enough (1/4)*(-4) = -1 is indeed the case. <BR>\n" );
document.write( "The answer has been verified.<BR>\n" );
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