document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92683>Question 92683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A line passes through the point P(-2,3) and has a slope of -1/2. What graph best represents the line? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67980 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=67980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are several ways you can do this problem. One way is to use the equation that says<BR>\n" );
document.write( "the slope m is equal to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y+-+y%5B1%5D%29%2F%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y+-+y%5B1%5D%29%2F%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where <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;\" > comes from the point P and is +3 and <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;\" > also comes from the point P<BR>\n" );
document.write( "and is -2. The problem also tells you that the slope 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;\" >.<BR>\n" );
document.write( "Substituting<BR>\n" );
document.write( "these values into the slope equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2+=+%28y+-+%28%2B3%29%29%2F%28x+-+%28-2%29%29 ALIGN=MIDDLE  ALT=\"-1%2F2+=+%28y+-+%28%2B3%29%29%2F%28x+-+%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2+=+%28y+-3%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"-1%2F2+=+%28y+-3%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this is an equation that can be used to graphically represent the line that has a slope<BR>\n" );
document.write( "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 have as one point (-2,3). You can find other points on that will be on<BR>\n" );
document.write( "the graph by assigning values to x and computing the corresponding values of y. For example,<BR>\n" );
document.write( "you can let x = 2. Substitute +2 for x and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2+=+%28y+-3%29%2F%282%2B2%29 ALIGN=MIDDLE  ALT=\"-1%2F2+=+%28y+-3%29%2F%282%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When you combine the 2+2 to get 4 in the denominator of the right side the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2+=+%28y-3%29%2F4 ALIGN=MIDDLE  ALT=\"-1%2F2+=+%28y-3%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you multiply both sides by 4 the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28-1%2F2%29+=+%284%2A%28y-3%29%29%2F4 ALIGN=MIDDLE  ALT=\"4%2A%28-1%2F2%29+=+%284%2A%28y-3%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side the produce of 4*(-1/2) = -2 and on the right side the 4 in the numerator <BR>\n" );
document.write( "cancels with the 4 in the denominator and you are left with just y-3. So the equation now<BR>\n" );
document.write( "is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+y+-+3 ALIGN=MIDDLE  ALT=\"-2+=+y+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can solve for y by adding +3 to both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1+=+y ALIGN=MIDDLE  ALT=\"%2B1+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So now you know that the point in which x equals 2 and y equals 1 is also on the graph.<BR>\n" );
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document.write( "So now you know two points on the line ... (-2,3) which was given in the problem and (2, 1)<BR>\n" );
document.write( "which you just calculated.  You can plot these two points and get the graph by drawing a <BR>\n" );
document.write( "straight line that goes through these two points.  <BR>\n" );
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document.write( "Another way that you could get an equation for that line is to use the slope intercept form<BR>\n" );
document.write( "of an equation. The slope intercept form is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+m%2Ax+%2B+b ALIGN=MIDDLE  ALT=\"y+=+m%2Ax+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which m is the slope and is given as <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;\" >. b is the value of y where the graph <BR>\n" );
document.write( "crosses the y-axis. Substituting the value of the slope into this slope<BR>\n" );
document.write( "intercept form <BR>\n" );
document.write( "results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x+%2B+b ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are given that the point (-2,3) is on the line. So you can substitute 3 for y and -2 for<BR>\n" );
document.write( "x into the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+%28-1%2F2%29%28-2%29+%2B+b ALIGN=MIDDLE  ALT=\"3+=+%28-1%2F2%29%28-2%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Doing the multiplication on the right side transforms the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+1++%2B+b ALIGN=MIDDLE  ALT=\"3+=+1++%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can now solve for b by subtracting 1 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+=+b ALIGN=MIDDLE  ALT=\"2+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now you can substitute this value for b and the slope value 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;\" > into the slope <BR>\n" );
document.write( "intercept form to get another equation for the graph:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the same equation as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F2%29+=+%28y+-3%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28-1%2F2%29+=+%28y+-3%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > that we got before. It's just in<BR>\n" );
document.write( "a little different form.  You can also get more points on the graph from the slope intercept<BR>\n" );
document.write( "form by assigning values to x and computing the corresponding value of y. Each time you do<BR>\n" );
document.write( "this you get another point on the graph. You can plot these points and connect them with<BR>\n" );
document.write( "a line that is then the graph you are looking for.<BR>\n" );
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document.write( "When you get done you should have a graph that looks like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%28-1%2F2%29x%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%28-1%2F2%29x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the graph crosses the y axis at +2, which is the value we found for b above.<BR>\n" );
document.write( "Also notice that the point (-2,3) is on the graph. Also notice that the slope of the graph<BR>\n" );
document.write( "is negative because it slopes down as you move to the right.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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