document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285372>Question 285372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i was asked draw a trend line and write an equation for my trend line in slope-intercept point. The problem is that i don't understand what's a trend line is and how to write an equation for that.\r<BR>\n" );
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document.write( "this is the problem:<BR>\n" );
document.write( "A giraffe was 1ft tall at birth. 7 ft tall at the age of 4, and 11 1/2 ft tall at the age of 7.\r<BR>\n" );
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document.write( "i was asked to make a scatter plot and i did.<BR>\n" );
document.write( "Please help me with my homework :( </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206880 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=206880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A trend line shows the average of a series of points over time.<BR>\n" );
document.write( "We can assume the independent variable, age, is the x-axis.<BR>\n" );
document.write( "That means height is a function of age, that is f(x), so it will be plotted on the y-axis.<BR>\n" );
document.write( "The data points you have are:<BR>\n" );
document.write( "(0,4)<BR>\n" );
document.write( "(4,7)<BR>\n" );
document.write( "(7,11.5)<BR>\n" );
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document.write( "To draw a line, you need two points.<BR>\n" );
document.write( "(0,4) should be one of them.<BR>\n" );
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document.write( "The slope-intercept form is:  y = mx+b<BR>\n" );
document.write( "In this case, we know that when x=0, y=4, so the y-intercept has to be 4.<BR>\n" );
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document.write( "The slope is the rise/run, which is the change in y divided by the change in x.<BR>\n" );
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document.write( "From (0,4) to (4,7),<BR>\n" );
document.write( "change in y = 7-4 = 3<BR>\n" );
document.write( "change in x = 4-0 = 4<BR>\n" );
document.write( "m = 3/4 = .75<BR>\n" );
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document.write( "From (4,7) to (7,11.5),<BR>\n" );
document.write( "change in y = 11.5-7 = 4.5<BR>\n" );
document.write( "change in x = 7-3 = 4<BR>\n" );
document.write( "slope = 4.5/4 = 1.25<BR>\n" );
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document.write( "So the slope is getting steeper, which means a straight line will have to miss one or both of the points.  That means the trend line will be somewhere between them.<BR>\n" );
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document.write( "We can pick the average value of 'x' and 'y' as the point that will be the second point on which we will base our trend line.<BR>\n" );
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document.write( "The average value of 'y' = (7+11.5)/2 = 18.5/2 = 9.25<BR>\n" );
document.write( "The average value of 'x' = (4+7)/2 = 11/2 = 5.5<BR>\n" );
document.write( "So the point is (5.5,9.25)<BR>\n" );
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document.write( "Based on the point (0,4) as our starting point...which reasonable since that is the at birth height...<BR>\n" );
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document.write( "change in y = 9.25-4 = 5.25<BR>\n" );
document.write( "change in x = 5.5-0 = 5.5<BR>\n" );
document.write( "slope = 5.25/5.5 = .954545<BR>\n" );
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document.write( "Recall our second point will be (5.5,9.25)<BR>\n" );
document.write( "The equation will be:<BR>\n" );
document.write( "y = .954545*x + 4<BR>\n" );
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