SOLUTION: The median age at 1st marriage for females increased from 24.5 years in 1995 to 25.1 in 2000 1995 will be year 5 and 2000 be year 10 Find equation of line through (5,24.5) and

Question 146077: The median age at 1st marriage for females increased from 24.5 years in 1995 to 25.1 in 2000 1995 will be year 5 and 2000 be year 10
Find equation of line through (5,24.5) and (10,25.1) What does X and Y represent in the equation? Interpret slope of this line and in what year will the median age be 30?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The median age at 1st marriage for females increased from 24.5 years in 1995 to 25.1 in 2000 1995 will be year 5 and 2000 be year 10
.
Find equation of line through (5,24.5) and (10,25.1) What does X and Y represent in the equation? Interpret slope of this line and in what year will the median age be 30?
.
First, find the equation of the line.
Start by finding the slope. Slope, given two points is:
(y2-y1)/(x2-x1)
=(25.1-24.5)/(10-5)
=(0.6)/(5)
=.6/5
.
Using the "slope-intercept" form of:
y = mx + b
where
m = slope
b = y-intercept
.
We will plug in one of the two points provided (say, (10,25.1)) doesn't matter which one along with the slope and solve for 'b' -- the y-intercept.
y = mx + b
25.1 = (.6/5)(10) + b
25.1 = 6/5 + b
125.5 = 6 + 5b
119.5 = 5b
23.9 = b
.
Recap we now know:
b = 23.9
m = .6/5
.
Plug it all back into:
y = mx + b
y = (.6/5)x + 23.9 <--this is your equation
.
The slope (since it is positive) shows that the age of a female getting married for the first time is increasing -- meaning women are gradually getting married later in life.
.
in what year will the median age be 30?
here, y = 30 and you're solving for x:
y = (.6/5)x + 23.9
30 = (.6/5)x + 23.9
6.1 = (.6/5)x
30.5 = .6x
50.833 = x
.
Since it is relative to 1990, we add:
1990+50.833 = 2040.833
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