Question 175894: The percentage of women in the 20–24 age
group who have never married went from 55% in 1970 to
73% in 2000 (Census Bureau, www.census.gov). Let 1970
be year 0 and 2000 be year 30.
a) Find and interpret the slope of the line through the
points (0, 55) and (30, 73).
b) Find the equation of the line in part (a).
c) What is the meaning of the y-intercept?
d) Use the equation to predict the percentage in 2010.
e) If this trend continues, then in what year will the
percentage of women in the 20–24 age group who have
never married reach 100%?
Answer by EMStelley(208)   (Show Source):
You can put this solution on YOUR website! For part a) you only need to know the equation for the slope of a line, which is
So, using the two points (0,55) and (30,73), we have that
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).
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
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%.
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
So the percentage should be 79% in 2010.
Lastly, for part e), they are asking for what x is y=100?
Subtract 55:
Divide by 3/5 (or multiply by 5/3):
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.
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