Question 58045This question is from textbook Elementary & Intermediate Algebra
: Please help me. The more I read the problem, the more I become confused. I appreciate your helping.
The percentage of women in the 20-24 age group who have never been married went from 55% in 1970 to 73% in 2000. 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). Find the equation of the line in part A. What is the meaning of the y-intercept? Use the equation to predit the percentage in 2010. If this trend continues, then in what year will the percentage of women in the 20-24 age group who have never been married reach 100%?
This question is from textbook Elementary & Intermediate Algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The percentage of women in the 20-24 age group who have never been married went from 55% in 1970 to 73% in 2000.
:
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).
:
Points(0,55) x1 = 0 and means the year 1970 (see above), y1 = 55 and means that
55% were unmarried. (30,73) x2 = 30 and means the year 2000, y2 = 73 and means that 73% were unmarried.
:
Find the the slope of the equation: m = (y2-y2)/(x2-x1)
:
m = (73-55)/(30-0) = 18/30 = 3/5 is the slope
:
Using the point/slope equation y - y1 = m(x - x1)
y - 55 = (3/5)(x - 0)
y = (3/5x) + 55
:
Find the equation of the line in part A.
See above: the equation is y = (3/5)x + 55
:
What is the meaning of the y-intercept? The y intercept is the value of y
when x = 0.
We can see from the above equation that when x = 0 then y will
equal 55:
i.e y = (3/5)0 + 55; y = 0 + 55 or just y = 55,
you could also say that it is the value of y when the graph crosses the y axis
(which occurs when x = 0).
Use the equation to predit the percentage in 2010.
The year 2010 is represented by the value after 1970. x = 2010-1970 = 40
:
Substitute 40 for x in our equation and solve for y
y = 3/5(40) + 55
y = 24 + 55
y = 79; 79% will be unmarried in the year 2010
:
If this trend continues, then in what year will the percentage of women in the 20-24 age group who have never been married reach 100%?
:
We can find this by substituting 100 for y and solving for x:
y = .6x + 55, converted 3/5 to decimal; .6
100 = .6x + 55
100 - 55 = .6(x)
45 = .6x
x = 45/.6
x = 75 yrs; 1970 + 75 = 2045 would be the year when none would be married
:
did this help you understand this stuff, you can email me if you have question
on this.
|
|
|
