document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146077>Question 146077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The median age at 1st marriage for females increased from 24.5 years in 1995  to 25.1 in 2000  1995 will be year 5 and 2000 be year 10\r<BR>\n" );
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document.write( "Find equation of line through (5,24.5) and (10,25.1) What does X and Y represent in the equation? Interpret slope of this line and in what year will the median age be 30? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106629 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=106629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The median age at 1st marriage for females increased from 24.5 years in 1995  to 25.1 in 2000  1995 will be year 5 and 2000 be year 10<BR>\n" );
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document.write( "Find equation of line through (5,24.5) and (10,25.1) What does X and Y represent in the equation? Interpret slope of this line and in what year will the median age be 30?<BR>\n" );
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document.write( "First, find the equation of the line.<BR>\n" );
document.write( "Start by finding the slope.  Slope, given two points is:<BR>\n" );
document.write( "(y2-y1)/(x2-x1)<BR>\n" );
document.write( "=(25.1-24.5)/(10-5)<BR>\n" );
document.write( "=(0.6)/(5)<BR>\n" );
document.write( "=.6/5<BR>\n" );
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document.write( "Using the \"slope-intercept\" form of:<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( "where<BR>\n" );
document.write( "m = slope<BR>\n" );
document.write( "b = y-intercept<BR>\n" );
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document.write( "We will plug in one of the two points provided (say, (10,25.1)) doesn't matter which one along with the slope and solve for 'b' -- the y-intercept.<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( "25.1 = (.6/5)(10) + b<BR>\n" );
document.write( "25.1 = 6/5 + b<BR>\n" );
document.write( "125.5 = 6 + 5b<BR>\n" );
document.write( "119.5 = 5b<BR>\n" );
document.write( "23.9 = b<BR>\n" );
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document.write( "Recap we now know:<BR>\n" );
document.write( "b = 23.9<BR>\n" );
document.write( "m = .6/5<BR>\n" );
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document.write( "Plug it all back into:<BR>\n" );
document.write( "y = mx + b<BR>\n" );
document.write( "y = (.6/5)x + 23.9  <--this is your equation<BR>\n" );
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document.write( "The slope (since it is positive) shows that the age of a female getting married for the first time is increasing -- meaning women are gradually getting married later in life.<BR>\n" );
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document.write( "in what year will the median age be 30?<BR>\n" );
document.write( "here, y = 30 and you're solving for x:<BR>\n" );
document.write( "y = (.6/5)x + 23.9<BR>\n" );
document.write( "30 = (.6/5)x + 23.9<BR>\n" );
document.write( "6.1 = (.6/5)x<BR>\n" );
document.write( "30.5 = .6x<BR>\n" );
document.write( "50.833 = x<BR>\n" );
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document.write( "Since it is relative to 1990, we add:<BR>\n" );
document.write( "1990+50.833 = 2040.833 </SPAN>\n" );
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