The percentage, Please HELP ME...!!?

Question

Single women. 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 1

1970+75 = 2045

Answer 2

a) We obtain the slope by dividing the change in the y direction by the change in the x direction.  (rise/run)

slope = (73-55)/(30-0) = 6/10

b) The equation is of the form y = ax + b ,where a = slope and b = y-intercept and x is the year.

y = (6/10)x + b  We plug in our first data point for  x = 0 and y = 55

55 = (6/10)(0) + b

55 = b

So our equation is  y = (6/10)x + 55

c)  The y-intercept is simply the value of y when x = 0.  This is the point where the equation intersects the y-axis.

d) 1970 corresponds to x = 0 Thus 2010 corresponds to x = 40

Now solve for y:

y = (6/10)(40)+55 = 79%

e)  We want to find x when y = 100

100 = (6/10)x + 55  Subtract 55 from both sides to get

45 = (6/10)x  Multiply both sides by 10/6

450/6 = x

75 = x

If we recall x = 0 corresponds to 1970 so x = 75 is 1970+75 = 2045