document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008979>Question 1008979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the line parallel to y=4/7x -2/7, which contains the given point (3,-5). I get stuck after solving for y and writing in slope-intercept form. The answer I get is y=4/7x - 12/7 - 20/7, which gives me y=4/7x - 32/7 and I know that's wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #624504 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=624504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> do it this way:\r<BR>\n" );
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document.write( "start with the general form of the slope intercept form of the equation for a straight line.\r<BR>\n" );
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document.write( "that is y = mx + b\r<BR>\n" );
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document.write( "m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "since the slope has to be the same as the original equation, then m = 4/7 and the equation becomes:\r<BR>\n" );
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document.write( "y = 4/7 * x + b\r<BR>\n" );
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document.write( "the point that you want to go through is (x,y) = (3,-5).\r<BR>\n" );
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document.write( "that means the x-coordinate is 3 and the y-coordinate is -5.\r<BR>\n" );
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document.write( "replace y with -5 and replace x with 3 and solve for b.\r<BR>\n" );
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document.write( "y = 4/7 * x + b becomes:\r<BR>\n" );
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document.write( "-5 = 4/7 * 3 + b\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "-5 = 12/7 + b\r<BR>\n" );
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document.write( "subtract 12/7 from both sides of this equation to get:\r<BR>\n" );
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document.write( "-5 - 12/7 = b\r<BR>\n" );
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document.write( "make common denominators to get:\r<BR>\n" );
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document.write( "-35/7 - 12/7 = b\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "-47/7 = b\r<BR>\n" );
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document.write( "your equation of y = 4/7 * x + b now becomes:\r<BR>\n" );
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document.write( "y = 4/7 * x - 47/7\r<BR>\n" );
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document.write( "that's your parallel line that goes through the point (3,-5).\r<BR>\n" );
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document.write( "here's a graph of that equation plus the original equation of y = 4/7 * x - 2/7.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/120804.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "red is the original equation.\r<BR>\n" );
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document.write( "blue is  the parallel equation that goes through the point (3,-5) as shown.\r<BR>\n" );
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document.write( "your alternative was to use the point slope form of the equation for a straight line.\r<BR>\n" );
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document.write( "the point slope form is y - y1 = m * (x - x1)\r<BR>\n" );
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document.write( "x1,y1 are the coordinates of the point that the line goes through.\r<BR>\n" );
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document.write( "your slope is 4/7 as before.\r<BR>\n" );
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document.write( "the equation becomes y - y1 = 4/7 * (x - x1)\r<BR>\n" );
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document.write( "your point that the line goes through is (3,-5)\r<BR>\n" );
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document.write( "replace y1 with -5 and replace x1 with 3 and you get:\r<BR>\n" );
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document.write( "y - (-5) = 4/7 * (x - 3)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "y + 5 = 4/7 * (x - 3)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "y + 5 = 4/7 * x - 3 * 4/7\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "y + 5 = 4/7 * x - 12/7\r<BR>\n" );
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document.write( "subtract 5 from both sides of the equation to get:\r<BR>\n" );
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document.write( "y = 4/7 * x - 12/7 - 5\r<BR>\n" );
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document.write( "make common denominators to get:\r<BR>\n" );
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document.write( "y = 4/7 * x - 12/7 - 35/7\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "y = 4/7 * x - 47/7\r<BR>\n" );
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document.write( "same equation as before only you used the point slope form of the equation to get it while before we used the slope intercept form to get it.\r<BR>\n" );
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document.write( "both ways are valid.\r<BR>\n" );
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document.write( "choose the one you feel more comfortable with.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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