document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203835>Question 203835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the slope-intercept equation of the line that is parallel to, -3x-5y=6 and has the same y-intercept as the graph of, 2x+y=-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153817 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=153817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the slope-intercept equation of the line that is parallel to: -3x-5y=6 and has the same y-intercept as the graph of:  2x+y=-4\r<BR>\n" );
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document.write( "Ok, first we have to write a line that is parallel to -3x - 5y = 6.   What you have to know is that parallel lines have the SAME slope.  So, we just have to find the slope of this line:   -3x - 5y = 6.   How do we do that?  Let's solve this equation for y and in doing so, we'll put the equation in slope/intercept form.  The slope intercept form is y = mx + b. In this form, the \"m\" is the slope.  So, let's go.......\r<BR>\n" );
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document.write( "First we solve for y:\r<BR>\n" );
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document.write( "-3x - 5y = 6  (add 3x to both sides)<BR>\n" );
document.write( "-5y = 3x + 6 (now divide both sides by -5 to isolate the y)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29y%2F-5+=+%283x%29%2F-5+%2B+%286%29%2F-5 ALIGN=MIDDLE  ALT=\"%28-5%29y%2F-5+=+%283x%29%2F-5+%2B+%286%29%2F-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3x%29%2F5+-+%286%29%2F5 ALIGN=MIDDLE  ALT=\"%28-3x%29%2F5+-+%286%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now can you see that your slope for the line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >?   Therefore, our next line that we create has to have this for a slope if the two lines are going to end up being parallel.\r<BR>\n" );
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document.write( "Now the next part of your problem says:  the line must have the same y-intercept as the graph of, 2x + y = -4.    Hmmmm... What is the y intercept of this line?   Here's something for you to know:\r<BR>\n" );
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document.write( "To find the y intercept, solve for y by making x = 0.<BR>\n" );
document.write( "To find the x intercept, solve for x by making y = 0.\r<BR>\n" );
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document.write( "SO in our equation:  2x + y = -4 <BR>\n" );
document.write( "We just need to solve for y by making x = 0. Let's try it:\r<BR>\n" );
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document.write( "2x + y = -4 (original equation)<BR>\n" );
document.write( "2(0) + y = -4<BR>\n" );
document.write( "0 + y = -4<BR>\n" );
document.write( "y = -4\r<BR>\n" );
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document.write( "SO we know that when x = 0, then y = -4.   Our y intercept is -4.\r<BR>\n" );
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document.write( "Now what do we want?  We want a line in the slope/intercept form (y = mx + b) and remember, that \"m\" is the slope.  What you also have to know is that \"b\" is the y intercept.  We want this new equation of a line to be parallel to the first line -3x - 5y = 6, which means the 2nd line must have (as we know from above) a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "SO let's plug in our info to the equation of:\r<BR>\n" );
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document.write( " y = mx + b<BR>\n" );
document.write( " y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%28-3%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - 4\r<BR>\n" );
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document.write( "Do you see how we \"plugged in\" the value for m, which was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well as the value for \"b\" which was -4?\r<BR>\n" );
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document.write( "Does that make sense for you?  I hope so. :-)\r<BR>\n" );
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