document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115771>Question 115771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for y in 6x-5y=-5. determine if the line is parallel to y=6/5x+5/9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84252 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=84252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One step at a time. First, solve the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+-+5y+=+-5 ALIGN=MIDDLE  ALT=\"6x+-+5y+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y:<BR>\n" );
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document.write( "Begin by getting rid of the term 6x on the left side so that you just have the term containing<BR>\n" );
document.write( "the y alone on the left side.  Do this by subtracting 6x from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5y+=+-6x+-+5 ALIGN=MIDDLE  ALT=\"-5y+=+-6x+-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are trying to solve for +y so at this point you may want to change the sign of -5y to +5y.<BR>\n" );
document.write( "You can do that by multiplying both sides of the equation (all terms) by -1 to change the<BR>\n" );
document.write( "equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+6x+%2B+5 ALIGN=MIDDLE  ALT=\"5y+=+6x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, solve for y by dividing both sides of this equation by 5 ... the multiplier of<BR>\n" );
document.write( "y to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%286%2F5%29%2Ax+%2B+5%2F5+=+%286%2F5%29%2Ax+%2B+1 ALIGN=MIDDLE  ALT=\"y+=+%286%2F5%29%2Ax+%2B+5%2F5+=+%286%2F5%29%2Ax+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the equation we now have is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=++%286%2F5%29%2Ax+%2B+1 ALIGN=MIDDLE  ALT=\"y+=++%286%2F5%29%2Ax+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this is in the slope-intercept form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which m, the multiplier of x, is the slope of the graph and b is the value on the y-axis<BR>\n" );
document.write( "where the graph crosses the y-axis. By comparing your equation with the slope intercept form<BR>\n" );
document.write( "you can see that the graph of your equation has a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F5%29 ALIGN=MIDDLE  ALT=\"%286%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it crosses the<BR>\n" );
document.write( "y-axis at the value of +1 on the y-axis.<BR>\n" );
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document.write( "Now look at the other equation you were given ... namely:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%286%2F5%29%2Ax+%2B+5%2F9 ALIGN=MIDDLE  ALT=\"y+=+%286%2F5%29%2Ax+%2B+5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Comparing this equation to the slope intercept form you will see that it also has a slope <BR>\n" );
document.write( "of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F5 ALIGN=MIDDLE  ALT=\"6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > but its graph crosses the y-axis at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F9 ALIGN=MIDDLE  ALT=\"5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "Now recognize that two graphs having the same slope but different crossing points on the<BR>\n" );
document.write( "y-axis are parallel lines that are always separated in vertical distance by an amount equal<BR>\n" );
document.write( "to the difference on the y-axis equal to the crossing points. The graph of the two equations<BR>\n" );
document.write( "shows this. The \"red\" graph is the graph of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%286%2F5%29%2Ax+%2B+1 ALIGN=MIDDLE  ALT=\"y+=+%286%2F5%29%2Ax+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the green<BR>\n" );
document.write( "graph is the graph of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%286%2F5%29%2Ax+%2B+5%2F9 ALIGN=MIDDLE  ALT=\"y+=+%286%2F5%29%2Ax+%2B+5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-15%2C15%2C-15%2C15%2C%286%2F5%29%2Ax+%2B+1%2C%286%2F5%29%2Ax+%2B+5%2F9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem and shows you that lines given by the two equations<BR>\n" );
document.write( "are actually parallel. <BR>\n" );
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