document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1063646>Question 1063646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here's another problem I have no clue how to do.\r<BR>\n" );
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document.write( "The point P (3,2) is on line L. The sum of the x and y intercepts of line L is 12. Find all possible equations for line L in standard form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #678779 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=678779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard form of a line is<BR>\n" );
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document.write( "Ax + By = C, where A, B, C are integers and A > 0<BR>\n" );
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document.write( "if x = 0, then y = C/B, this is the y intercept<BR>\n" );
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document.write( "if y = 0, then x = C/A, this is the x intercept<BR>\n" );
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document.write( "For line L, we know that<BR>\n" );
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document.write( "1) C/A + C/B = 12<BR>\n" );
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document.write( "using point (3,2)<BR>\n" );
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document.write( "2) 3A + 2B = C<BR>\n" );
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document.write( "We have three points on Line L - (3, 2), (C/A, 0), (0, C/B) <BR>\n" );
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document.write( "slope(m) = (y2 - y1) / (x2 - x1) = ( 3 - 0) / (2 - C/B) = 3 / (2 - C/B)<BR>\n" );
document.write( "slope(m) = (3 - C/A) / 2<BR>\n" );
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document.write( "set both equations for m equal to each other<BR>\n" );
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document.write( "(3 - C/A) / 2 = 3 / (2 - C/B)<BR>\n" );
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document.write( "from equation 1) we know that C/A = 12 - C/B<BR>\n" );
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document.write( "let C/B = k, then<BR>\n" );
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document.write( "6 = (3 - 12 + k) * ( 2 - k)<BR>\n" );
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document.write( "6 = (-9 + k) * (2 - k) = -18 +11k -k^2<BR>\n" );
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document.write( "k^2 -11k +24 = 0<BR>\n" );
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document.write( "(k - 8) * (k - 3) = 0<BR>\n" );
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document.write( "there are two possible values to consider<BR>\n" );
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document.write( "C/B = 8<BR>\n" );
document.write( "C/B = 3<BR>\n" );
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document.write( "C/A + 8 = 12, C/A = 4 and C = 8B<BR>\n" );
document.write( "4A = 8B<BR>\n" );
document.write( "A = 2B<BR>\n" );
document.write( "2Bx + Bx = 8B<BR>\n" );
document.write( "2x +y = 8<BR>\n" );
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document.write( "C/A + 3 = 12, C/A = 9, C = 3B<BR>\n" );
document.write( "9A = 3B<BR>\n" );
document.write( "A = B/3<BR>\n" );
document.write( "Bx/3 + By = 3B<BR>\n" );
document.write( "x + 3y = 9<BR>\n" );
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document.write( "2x + y = 8<BR>\n" );
document.write( "x + 3y = 9<BR>\n" );
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document.write( ":\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );