document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204789>Question 204789</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the line that contains the points (2, 2) and (-3, 12). \r<BR>\n" );
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document.write( "Here is part of the answer. Can you identify the missing part? \r<BR>\n" );
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document.write( "y = -2x + ___ \r<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 #154565 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=154565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the line that contains the points (2, 2) and (-3, 12). <BR>\n" );
document.write( "Here is part of the answer. Can you identify the missing part? <BR>\n" );
document.write( "y = -2x + ___ \r<BR>\n" );
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document.write( "In this problem, you need to first find the SLOPE, and the way to find that is to use this formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "SO let's determine the slope.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812+-+2%29%2F%28-3+-+2%29 ALIGN=MIDDLE  ALT=\"%2812+-+2%29%2F%28-3+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F-5 ALIGN=MIDDLE  ALT=\"10%2F-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is -2.   <BR>\n" );
document.write( "SO now we know our slope is -2.  <BR>\n" );
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document.write( "The next thing we have to do is use the POINT SLOPE equation of a line.  We use this equation when we know the slope and when we know a point that the line must go thru.  We just learned that the slope is -2.   Generally, the slope is represented by the variable \"m\".   \r<BR>\n" );
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document.write( "AND we know that in this case, the line contains the points (2, 2) and (-3, 12). You can use either of these points, but for our purposes, I'm just going to choose the point (2, 2).\r<BR>\n" );
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document.write( "SO... we have to use the point slope formula, right?  Ok, that formula is this:\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( "Soooooooooo, all you have to do is fill in the blanks for what you know.  You know that m = -2 right?  And you know that the line goes thru (2, 2), right?  SO let's fill in the blanks.  Here goes:\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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+2%29 ALIGN=MIDDLE  ALT=\"%28y+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x+-+2%29 ALIGN=MIDDLE  ALT=\"-2%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see where I filled in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > info?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+2 ALIGN=MIDDLE  ALT=\"y+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x+%2B+4 ALIGN=MIDDLE  ALT=\"-2x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I distributed the -2 to the \"x\" and to the -2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2x+%2B+4+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+-2x+%2B+4+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Now I added +2 to both sides to isolate the y)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2x+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+-2x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (I added 4 + 2 = 6)\r<BR>\n" );
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document.write( "SOooooo now we have a final answer.  We have that an equation of the line that contains the points (2, 2) and (-3, 12).\r<BR>\n" );
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document.write( "As you know, when we tried to solve this problem, we used the POINT SLOPE equation of a line.  However, at the end, we did the math you saw above (where we distributed the -2 etc) and when we did that math, we put the equation of the line in the SLOPE INTERCEPT equation of a line.\r<BR>\n" );
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document.write( "THEREFORE....when the question asks if you can identify the missing part, you can say that the missing part is the Y INTERCEPT, which is 6.\r<BR>\n" );
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document.write( "WHY can we say that?  Well, the SLOPE INTERCEPT form of a line is y = mx + b and in this equation, \"m\" is the slope and \"b\" is the y-intercept.  \r<BR>\n" );
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document.write( "Our line, if you remember is:  y = -2x + 6.   Do you see that \"m\" (the slope) is -2 and \"b\" (the y intercept) is + 6?   \r<BR>\n" );
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document.write( "SO now you have your answer.  I hope this helps! :-) </SPAN>\n" );
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