Question 175894
For part a) you only need to know the equation for the slope of a line, which is
{{{m=(y_2-y_1)/(x_2-x_1)}}}
So, using the two points (0,55) and (30,73), we have that
{{{m=(73-55)/(30-0)=18/30=3/5}}}
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
{{{y-55=(3/5)(x-0)}}}
{{{y-55=(3/5)x}}}
{{{y=(3/5)x+55}}}
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
{{{y=(3/5)(40)+55=79}}}
So the percentage should be 79% in 2010.
Lastly, for part e), they are asking for what x is y=100?
{{{100=(3/5)x+55}}}
Subtract 55:
{{{45=(3/5)x}}}
Divide by 3/5 (or multiply by 5/3):
{{{75=x}}}
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.