document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071591>Question 1071591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an equation in standard form for a line passing through the pair of points. (-8,0) and (0,3).<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686488 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=686488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Standard form is Ax + By = C   where A,B,and C are constants (often integers).\r<BR>\n" );
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document.write( "Point-slope form is  y = mx + b, where m=slope and b=y-intercept (i.e. value at x=0).\r<BR>\n" );
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document.write( "I've always found it easiest to work in point-slope form, then rearrange it to standard form at the end.   Given the two points, the slope can be found as rise/run (change in y value over change in x):<BR>\n" );
document.write( "[ It does not matter which point you use as start/end, but once you decide which point to use as the \"end\", be sure to use the companion y value as the ending y value ]\r<BR>\n" );
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document.write( "             m = (y2-y1)/(x2-x1) <BR>\n" );
document.write( "             m = (3-0)/(0-(-8)) = 3/8\r<BR>\n" );
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document.write( "[ If we used the points the other way —> m = (0-3)/(-8-0) = -3/-8 = 3/8 ]\r<BR>\n" );
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document.write( "So far we have:<BR>\n" );
document.write( "     y = (3/8)x + b\r<BR>\n" );
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document.write( "To find 'b', choose one of the points, say (-8,0), then plug in and solve for b:   <BR>\n" );
document.write( "       0 = (3/8)(-8) + b  —>  0 = -3 + b —> b=3\r<BR>\n" );
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document.write( "        Now we have <BR>\n" );
document.write( "            y = (3/8)x + 3\r<BR>\n" );
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document.write( " Re arranging to standard form:\r<BR>\n" );
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document.write( "                -(3/8)x + y = 3<BR>\n" );
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document.write( "Technically, the above is acceptable.  Some teachers may want you to make the coefficients integers if possible, and some *think* the coefficient in front of x should be positive (my Calculus book does not say this is a requirement).   So here are other forms that are equally valid:\r<BR>\n" );
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document.write( "Multiply through by 8:<BR>\n" );
document.write( "             -3x + 8y = 24    (probably what most teachers expect)\r<BR>\n" );
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document.write( "Multiply through by -1:<BR>\n" );
document.write( "               3x - 8y = -24   (some teachers may want to see it expressed like this, A>0)\r<BR>\n" );
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document.write( "Good luck!\r<BR>\n" );
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