Find linear models for each set of data. In what year will the two quantities be equal?
Year-1970 1975 1980 1985 1990 1995 2000
men (years) 67.6 69.3 70.4 71.6 72.2 72.8 74.9
women (years) 75.1 76.8 77.5 78.2 78.8 79.2 79.9
Let x be the number of years since 1970. What is the linear model for men?
y=__x+___
To find the linear model for men, we need to find the equation of the line that best fits the data points (x, y), where x is the number of years since 1970 and y is the respective men's life expectancy.
First, let's calculate the slope of the line:
Slope (m) = (men's life expectancy in 2000 - men's life expectancy in 1970) / (years in 2000 - years in 1970)
= (74.9 - 67.6) / (2000 - 1970)
= 7.3 / 30
Then, let's choose any point on the line and write the linear equation using the point-slope form:
(x1, y1) = (0, men's life expectancy in 1970) = (0, 67.6)
y - y1 = m(x - x1)
y - 67.6 = (7.3 / 30)(x - 0)
y - 67.6 = (7.3 / 30)x
y = (7.3 / 30)x + 67.6
So, the linear model for men is:
y = (7.3 / 30)x + 67.6
Now, let's find out in what year the men's and women's life expectancies will be equal.
We can set the two equations equal to each other and solve for x:
(7.3 / 30)x + 67.6 = (7.3 / 30)x + b
We can cancel out the (7.3 / 30) on both sides:
b = 67.6
Therefore, the two quantities will be equal in any year since 1970.