Use the coordinates of the two points that show male life expectancies for 1980 and 2000 to write a linear
function that models life expectancy. E (x), for men born in this community x years after 1960
Coordinates are
1960-66.8
1970-67.5
1980-69.9
1990-70.5
2000-74.1
2004-75.2
E(x) = 0.5x + 66.3
To write a linear function that models life expectancy for men born in this community, we can use the two given points: (1980, 69.9) and (2000, 74.1).
The general form of a linear function is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To find the slope (m) of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's denote (x1, y1) as (1980, 69.9) and (x2, y2) as (2000, 74.1):
m = (74.1 - 69.9) / (2000 - 1980)
m = 4.2 / 20
m = 0.21
Now that we have the slope, we can substitute it into the general linear function equation:
y = 0.21x + b
To find the y-intercept (b), we can substitute one of the given points into the equation.
Let's use the point (1980, 69.9):
69.9 = 0.21 * 1980 + b
69.9 = 415.8 + b
To isolate b, we subtract 415.8 from both sides:
b = 69.9 - 415.8
b = -345.9
Now, we have our linear function to model life expectancy for men born in this community x years after 1960:
E(x) = 0.21x - 345.9
To create a linear function that models life expectancy for men born x years after 1960, we can use the coordinates for 1980 and 2000.
The coordinates are as follows:
1980 - Life Expectancy: 69.9
2000 - Life Expectancy: 74.1
Let's assign the year after 1960 as 'x', and the life expectancy as 'E(x)'. We can use the slope-intercept form of a linear equation, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
To find the slope, we'll use the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (1980, 69.9) and (2000, 74.1), we get:
m = (74.1 - 69.9) / (2000 - 1980)
= 4.2 / 20
= 0.21
So, the slope 'm' is 0.21.
Next, we need to find the y-intercept 'b'. We can use any of the given coordinates. Let's use the coordinate (1980, 69.9):
69.9 = 0.21 * 1980 + b
Simplifying this equation, we get:
b = 69.9 - (0.21 * 1980)
= 69.9 - 415.8
= -345.9
Now, we can write the equation for the life expectancy of men born x years after 1960:
E(x) = 0.21x - 345.9
This linear function models the life expectancy based on the given coordinates for men born x years after 1960.