document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250242>Question 250242</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble with how to find the equation of the line. <BR>\n" );
document.write( "Here is the problem: <BR>\n" );
document.write( "Find the equation of the line parallel to 2x+4y=9 and passing through the point (6,-2).\r<BR>\n" );
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document.write( "If someone could walk me through the steps on how to find the answer i would really appreciate it i have a final in two days! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182172 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=182172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's take this a step at a time:\r<BR>\n" );
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document.write( "You want a line parallel to 2x+4y =9.  So the first thing you have to know is lines that are parallel have the SAME slope.  \r<BR>\n" );
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document.write( "Therefore, you have to find the slope for the equation, 2x + 4y = 9.  How can you do that?  \r<BR>\n" );
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document.write( "Let's change the equation to the y = mx + b format (the slope intercept form of a line) where \"m\" is the slope.  If we want to put the equation into y = mx + b format, we have to solve for \"y\".  SO here goes:\r<BR>\n" );
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document.write( "2x+ 4y = 9  (your original equation)<BR>\n" );
document.write( "4y = -2x + 9  (subtracted 2x from both sides to isolate the y)\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2F4 ALIGN=MIDDLE  ALT=\"-2x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4 ALIGN=MIDDLE  ALT=\"9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (divided both sides by 4 to isolate the y)\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2x ALIGN=MIDDLE  ALT=\"-1%2F2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4 ALIGN=MIDDLE  ALT=\"9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (simplified the fraction of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F4 ALIGN=MIDDLE  ALT=\"-2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now we can see that the slope of the line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >}.  Therefore, any line parallel to that line must ALSO have a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now to the next step:\r<BR>\n" );
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document.write( "Your new line must also go thru the point   (6, -2)\r<BR>\n" );
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document.write( "When you know the point that a line must go thru and the slope you want, then you just \"plug\" this info into the point/slope form of a line.  The point slope form of a line is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+y%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y+-+y%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%28x++-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m%28x++-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "SO let's plug in our info:\r<BR>\n" );
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document.write( "We want a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we want it to go thru point (6, -2)\r<BR>\n" );
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document.write( "y - -2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 6)  \r<BR>\n" );
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document.write( "y - -2 is really y + 2 so let's rewrite the above and then do the math.\r<BR>\n" );
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document.write( "y + 2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 6)  If your teacher wants the answer in \"point/slope\" form, you are finished at this step.  If the teacher wants the answer in slope/intercept form, then you have to do more thinking.  You'd have to do this:\r<BR>\n" );
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document.write( "y + 2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x - 6)  (equation in point/slope form)<BR>\n" );
document.write( "y + 2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2x ALIGN=MIDDLE  ALT=\"-1%2F2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 3   (distributed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2x ALIGN=MIDDLE  ALT=\"-1%2F2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 3 - 2 (subtracted 2 from both sides of the equation)\r<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2x ALIGN=MIDDLE  ALT=\"-1%2F2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1 (equation in slope intercept form)\r<BR>\n" );
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document.write( "I think that's everything.  I hope it helps you and good luck on your final. :-) </SPAN>\n" );
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