Question

the graph gives the number of additional years of life expectancy at age 65 for selected years from 1950 projected to 2050. complete parts (a) through (e)
all graphs have viewing window 0, 110 by 0, 25, xscl = 10, yscl = 5
b. find a linear function that models the data, with y equal to the life expectancy and x equal to the number of years after 1950.
y = (square)x+(square)
(type integers or decimals rounded to three decimal places as needed.)

Explanation:

Step1: Select two points

Let's take the points (0, 14.1) (corresponding to year 1950 with life - expectancy 14.1) and (100, 21.4) (corresponding to year 2050 with life - expectancy 21.4).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=14.1,x_2 = 100,y_2 = 21.4$. So $m=\frac{21.4 - 14.1}{100-0}=\frac{7.3}{100}=0.073$.

Step3: Find the y - intercept $b$

The equation of a line is $y=mx + b$. Using the point (0, 14.1), when $x = 0,y=14.1$. Substituting into $y=mx + b$, we get $b = 14.1$ since $y=m\times0 + b$ when $x = 0$.

Answer:

$y = 0.073x+14.1$