# Thread: Find a linear function that fits the data word problem

1. ## Find a linear function that fits the data word problem

in 1990 the life expectancy of females (in the U.S.) was 78.8. in the year 2000, it was 79.8. let f(t) represent the life expectancy and t the number of years since 1990.
a. Find a linear function that fits the data.
b. Use this function to estimate the life expectancy of females in 2008

in 1990 the life expectancy of females (in the U.S.) was 78.8. in the year 2000, it was 79.8. let f(t) represent the life expectancy and t the number of years since 1990.
a. Find a linear function that fits the data.
let $t$ be the years since 1990. and we write our points as $(t,f(t))$

we have the point $(0,78.8)$ since in 1990 (when t = 0) the life expectancy (f(t)) was 78.8

and the point $(10,79.8)$ by a similar reasoning.

now we simply need to find the equation of the line that passes through these two points.

the slope is given by: $m = \frac {f(10) - f(0)}{10 - 0}$

and we can find the line using the point slope form:

$y - y_1 = m(t - t_1)$

here $(t_1,y_1)$ is one of the points the line passes through. plug in the values and solve for $y$ (which is $f(t)$)

b. Use this function to estimate the life expectancy of females in 2008