document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133871>Question 1133871</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y varies inversely with x. if y=-6 when x=-2 find y when x=5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751123 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for inverse variation is y = k/x.\r<BR>\n" );
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document.write( "solve for k and you get k = xy.\r<BR>\n" );
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document.write( "k is the constant of variation.\r<BR>\n" );
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document.write( "it always remains the same.\r<BR>\n" );
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document.write( "what this means is, if you multiply x by some factor, you need to divide y by the same factor.\r<BR>\n" );
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document.write( "for example, let x = 4 and y = 8\r<BR>\n" );
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document.write( "the constant of variation is 4 * 8 = 32\r<BR>\n" );
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document.write( "if you multiply 4 by 2, then you have to divide 8 by 2.\r<BR>\n" );
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document.write( "you will get 8 * 4 = 32.\r<BR>\n" );
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document.write( "k has to stay the same.\r<BR>\n" );
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document.write( "that is what is meant by the constant of variation.\r<BR>\n" );
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document.write( "the formula for direct variation is y = k * x\r<BR>\n" );
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document.write( "solve for k to get k = y / x.\r<BR>\n" );
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document.write( "if you multiply y by some factor, you also have to multiply x by the same factor in order to keep k the same.\r<BR>\n" );
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document.write( "for example, let x = 4 and y = 8.\r<BR>\n" );
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document.write( "y / x = 2 = k\r<BR>\n" );
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document.write( "if you multiply y by 2, you have to multiply x by 2 as well in order to keep k constant.\r<BR>\n" );
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document.write( "you will get 16 / 8 = 2.\r<BR>\n" );
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document.write( "the same concept applies whether or not the values involved are positive or minus.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = -2, y = -6\r<BR>\n" );
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document.write( "k = -2 * -6 = 12\r<BR>\n" );
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document.write( "that's your constant of variation.\r<BR>\n" );
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document.write( "if x doubles, then y must be cut in half.\r<BR>\n" );
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document.write( "so when x becomes -4, y must becomes -3.\r<BR>\n" );
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document.write( "k = xy becomes -4 * -4 = 12.\r<BR>\n" );
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document.write( "k is constant.\r<BR>\n" );
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document.write( "what happens when x becomes 4.\r<BR>\n" );
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document.write( "4 * y = 12 in order to keep k constant.\r<BR>\n" );
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document.write( "solve for y to get y = 3.\r<BR>\n" );
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document.write( "when x = -2, y = -6<BR>\n" );
document.write( "when x = -4, y = -3<BR>\n" );
document.write( "when x = 4, y = 3\r<BR>\n" );
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document.write( "the constant of variation was always 12.<BR>\n" );
document.write( "x * y = k<BR>\n" );
document.write( "if x is multiplied by a factor, y must be divided by the same factor in order to keep k constant.\r<BR>\n" );
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document.write( "this can be seen graphically below.\r<BR>\n" );
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document.write( "your problem states:\r<BR>\n" );
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document.write( "if y = -6 when x = -2, find y when x = 5.\r<BR>\n" );
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document.write( "the formula is the same.\r<BR>\n" );
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document.write( "y = k / x\r<BR>\n" );
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document.write( "solve for k to get k = y * x.\r<BR>\n" );
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document.write( "when y = -6 and x = -2, you get k = 12\r<BR>\n" );
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document.write( "what happens when x = 5?\r<BR>\n" );
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document.write( "x * y = 12\r<BR>\n" );
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document.write( "when x = 5, the formula becomes 5 * y = 12\r<BR>\n" );
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document.write( "solve for y to get y = 12/5 = 2.4\r<BR>\n" );
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document.write( "-2 * -6 = 12<BR>\n" );
document.write( "5 * 2.4 = 12\r<BR>\n" );
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document.write( "the constant of variation is always k.\r<BR>\n" );
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document.write( "you multiplied -2 by -2.5 to get 5.<BR>\n" );
document.write( "you divided -6 by -2.5 to get 2.4.\r<BR>\n" );
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document.write( "inverse variation says that whatever you multiply x1 by to get x2, you need to divide y1 by to get y2.\r<BR>\n" );
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document.write( "in your problem, x1 was -2 and y1 was -6 while x2 was 5 and y2 was 2.4\r<BR>\n" );
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document.write( "you multiplied x1 by -2.5 to get x2 (-2 * -2.5 = 5)<BR>\n" );
document.write( "you divided y1 by -2.5 to get y2 (-6 / -2.5 = 2.4)\r<BR>\n" );
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document.write( "this can be seen graphically below.\r<BR>\n" );
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