document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159296>Question 1159296</A>: <I><SPAN STYLE=\"word-break: break-all;\">  I'm trying to figure out this problem to help my son with his homework. \r<BR>\n" );
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document.write( "Write the equation of a line that passes through (-2,-1) and (2,3).<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 #782290 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=782290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red size=4>y = x + 1</font><BR>\n" );
document.write( "slope = 1, y intercept = 1<BR>\n" );
document.write( "You can think of y = x+1 as y = 1x + 1\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "Find the slope of the line through (x1,y1) = (-2,-1) and (x2,y2) = (2,3)<BR>\n" );
document.write( "m = (y2 - y1)/(x2 - x1)<BR>\n" );
document.write( "m = (3 - (-1))/(2 - (-2))<BR>\n" );
document.write( "m = (3 + 1)/(2 + 2)<BR>\n" );
document.write( "m = 4/4<BR>\n" );
document.write( "m = 1\r<BR>\n" );
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document.write( "Plug m = 1 and (x1,y1) = (-2,-1) into the point slope formula. Solve for y.<BR>\n" );
document.write( "y - y1 = m(x - x1)<BR>\n" );
document.write( "y - (-1) = 1(x - (-2)) ... substitution<BR>\n" );
document.write( "y + 1 = 1(x + 2) ... subtracting a negative is the same as adding<BR>\n" );
document.write( "y + 1 = x + 2<BR>\n" );
document.write( "y + 1 - 1 = x + 2 - 1 ... subtract 1 from both sides to isolate y<BR>\n" );
document.write( "y = x + 1\r<BR>\n" );
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document.write( "To confirm we have the correct answer, lets test out the point (-2, -1). This means x = -2 and y = -1 pair up together<BR>\n" );
document.write( "y = x+1<BR>\n" );
document.write( "-1 = -2+1 ... replace x with -2, y with -1<BR>\n" );
document.write( "-1 = -1 ... true equation<BR>\n" );
document.write( "since we get a true equation (ie the same number on both sides), this means we have confirmed (-2,-1) as a solution. Let's check the other ordered pair.\r<BR>\n" );
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document.write( "Plug in (x,y) = (2,3)<BR>\n" );
document.write( "y = x+1<BR>\n" );
document.write( "3 = 2+1 ... replace x with 2, y with 3<BR>\n" );
document.write( "3 = 3 ... also true<BR>\n" );
document.write( "We have confirmed both points, so this fully confirms the answer.\r<BR>\n" );
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document.write( "If you wish to have the equation in standard form (Ax+By = C), then one way is to do the following steps<BR>\n" );
document.write( "y = x + 1<BR>\n" );
document.write( "y-x = x+1-x ... subtract x from both sides<BR>\n" );
document.write( "-x+y = 1<BR>\n" );
document.write( "-x+y = 1 .... technically this is in standard form, but many books require that A > 0<BR>\n" );
document.write( "-1(-x+y) = -1*1 ... to make A > 0, multiply both sides by -1<BR>\n" );
document.write( "x-y = -1 ... distribute and multiply\r<BR>\n" );
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document.write( "x-y = -1 is in the form Ax+By = C where A = 1, B = -1, C = -1<BR>\n" );
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