document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175894>Question 175894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The percentage of women in the 20–24 age<BR>\n" );
document.write( "group who have never married went from 55% in 1970 to<BR>\n" );
document.write( "73% in 2000 (Census Bureau, www.census.gov). Let 1970<BR>\n" );
document.write( "be year 0 and 2000 be year 30.<BR>\n" );
document.write( "a) Find and interpret the slope of the line through the<BR>\n" );
document.write( "points (0, 55) and (30, 73).<BR>\n" );
document.write( "b) Find the equation of the line in part (a).<BR>\n" );
document.write( "c) What is the meaning of the y-intercept?<BR>\n" );
document.write( "d) Use the equation to predict the percentage in 2010.<BR>\n" );
document.write( "e) If this trend continues, then in what year will the<BR>\n" );
document.write( "percentage of women in the 20–24 age group who have<BR>\n" );
document.write( "never married reach 100%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131024 by </B><A HREF=/tutors/aboutme.mpl?userid=EMStelley><B>EMStelley(208)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EMStelley><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=EMStelley><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=131024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For part a) you only need to know the equation for the slope of a line, which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y_2-y_1%29%2F%28x_2-x_1%29 ALIGN=MIDDLE  ALT=\"m=%28y_2-y_1%29%2F%28x_2-x_1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, using the two points (0,55) and (30,73), we have that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%2873-55%29%2F%2830-0%29=18%2F30=3%2F5 ALIGN=MIDDLE  ALT=\"m=%2873-55%29%2F%2830-0%29=18%2F30=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What does this mean?  It means for every 5 unit gain in x, the y will raise by 3.  So in the context of this question, a change of five years would correspond to a change of 3% (of women in the age group 20-24 who have never married).<BR>\n" );
document.write( "For part b), now that you have the slope, and two points, you can write the equation of the line using the point-slope equation.  Let's use (0,55) as our point.  Then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-55=%283%2F5%29%28x-0%29 ALIGN=MIDDLE  ALT=\"y-55=%283%2F5%29%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-55=%283%2F5%29x ALIGN=MIDDLE  ALT=\"y-55=%283%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F5%29x%2B55 ALIGN=MIDDLE  ALT=\"y=%283%2F5%29x%2B55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For part c), we have to think about how the y-intercept is found.  The y-intercept can be found by setting x to 0.  We know that this is 55, since we are given that point in the question.  So when x=0 (1970), the percentage of women in that age group who have never married was 55%.<BR>\n" );
document.write( "For part d), we are supposed to predict the percentage in 2010.  If 1970 is x=0, then 2010 is x=2010-1970=40.  So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F5%29%2840%29%2B55=79 ALIGN=MIDDLE  ALT=\"y=%283%2F5%29%2840%29%2B55=79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the percentage should be 79% in 2010.<BR>\n" );
document.write( "Lastly, for part e), they are asking for what x is y=100?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=%283%2F5%29x%2B55 ALIGN=MIDDLE  ALT=\"100=%283%2F5%29x%2B55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 55:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45=%283%2F5%29x ALIGN=MIDDLE  ALT=\"45=%283%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide by 3/5 (or multiply by 5/3):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75=x ALIGN=MIDDLE  ALT=\"75=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Last, we need to convert this back into a year.  Since x=0 corresponds to 1970, we simply add 75 to 1970, resulting in the year 2045. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );