Questions: The bar graph gives the life expectancy for men in a certain community born in six selected years. Complete parts a through c. Use the coordinates of the two points that show male life expectancies for 1980 and 2000 to write a linear function that models life expect E(x), for men born in this community x years after 1960. E(x)= (Use integers or decimals for any numbers in the expression. Type your answer in slope-intercept form.)

Solution Steps

The question asks for a linear function that models life expectancy for men born in 1980 and 2000. The x-axis represents the years after 1960, and the y-axis represents the life expectancy.

For 1980, the x-coordinate is 1980 - 1960 = 20. From the bar graph, the life expectancy in 1980 is 69.9, so the y-coordinate is 69.9. Thus, the first point is (20, 69.9).

For 2000, the x-coordinate is 2000 - 1960 = 40. From the bar graph, the life expectancy in 2000 is 71.8, so the y-coordinate is 71.8. Thus the second point is (40, 71.8).

The slope, m, of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (20, 69.9) and (40, 71.8):

m = (71.8 - 69.9) / (40 - 20) m = 1.9 / 20 m = 0.095

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We can use one of the points and the calculated slope to find the y-intercept:

Using the point (20, 69.9) and m = 0.095:

69.9 = 0.095 * 20 + b 69.9 = 1.9 + b b = 69.9 - 1.9 b = 68

Final Answer: The linear function is E(x) = 0.095x + 68