document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186791>Question 1186791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> So I have to solve for the direct variation and then graph -2y = 5x, and I am completely lost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817764 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=817764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> direct variation formula is y = k * x\r<BR>\n" );
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document.write( "k is the constant of variation.<BR>\n" );
document.write( "you first solve for k and then you use k to solve for the rest of the problem.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "y is directly proportional to x.\r<BR>\n" );
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document.write( "y = 25 when x = 5\r<BR>\n" );
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document.write( "formula is y = k * x<BR>\n" );
document.write( "when x = 3, y = 25.\r<BR>\n" );
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document.write( "replace y with 25 and x with 5 and solve for k.<BR>\n" );
document.write( "y = k * x becomes:<BR>\n" );
document.write( "25 = k * 5<BR>\n" );
document.write( "solve for k to get:<BR>\n" );
document.write( "k = 25/5 = 5.\r<BR>\n" );
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document.write( "when k = 5, 25 = k * 5 becomes 25 = 5 * 5 which becomes 25 = 25.<BR>\n" );
document.write( "this confirms the value of k is good.\r<BR>\n" );
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document.write( "what is the value of y when x becomes 30.<BR>\n" );
document.write( "the value of k is used to help solve this.<BR>\n" );
document.write( "y = k * x becomes y = 5 * 30 which becomes y = 150.\r<BR>\n" );
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document.write( "note that 25 is equal to 5 * 5 and 150 is equal to 5 * 30.<BR>\n" );
document.write( "that's direct variation.<BR>\n" );
document.write( "as x increases, y increases by the same proportion.<BR>\n" );
document.write( "y = 5  * x<BR>\n" );
document.write( "x = 5, y = 25<BR>\n" );
document.write( "x = 30, y = 150\r<BR>\n" );
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document.write( "to graph -2y = 5x, you have to solve for y.<BR>\n" );
document.write( "divide both sides of the equation by -2 to get:<BR>\n" );
document.write( "y = 5x / -2.<BR>\n" );
document.write( "this can be shown as:<BR>\n" );
document.write( "y = -5/2 * x\r<BR>\n" );
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document.write( "that equations is now in slope intercept form of y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.<BR>\n" );
document.write( "the slope is equal to -5/2<BR>\n" );
document.write( "the y-intercept is 0.\r<BR>\n" );
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document.write( "the graph of that equation looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/102701.jpg\" >\r<BR>\n" );
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document.write( "in the graph you can see two points plotted.\r<BR>\n" );
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document.write( "points are plotted in (x,y) format.\r<BR>\n" );
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document.write( "(0,0) says the value of y is 0 when the value of x is 0.<BR>\n" );
document.write( "that's the y-intercept.\r<BR>\n" );
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document.write( "(10,-25) says the value of y is -25 when the value of x is 10.\r<BR>\n" );
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document.write( "from the equation of y = -5/2 * x, then x = 10, y = -5/2 * 10 which makes y = -25.\r<BR>\n" );
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document.write( "the slope is the change in the value of y divided by the corresponding change in the value of x.\r<BR>\n" );
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document.write( "the starting point was (0,0) and the ending point was (10,-25)<BR>\n" );
document.write( "x went from 0 to 10.<BR>\n" );
document.write( "y went from 0 to -25.<BR>\n" );
document.write( "the slope is the change in y divided by the corresponding change in x.<BR>\n" );
document.write( "-25/10 = -5/2 which is the slope of the equation.\r<BR>\n" );
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document.write( "here's some references that might help.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/variatn.htm\" target = \"_blank\">https://www.purplemath.com/modules/variatn.htm</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/strtlneq.htm\" target = \"_blank\">https://www.purplemath.com/modules/strtlneq.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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