Question 58045
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
:
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