in 1993, the life expectancy of males in a certain country was 70.7. in 1999, it was 74.6 year. Let E represent the life expectancy in year t and let t represent the number of years since 1993.
E(t) = ?t + ?
I'm assuming this is a linear function? "E(t) = ?t + ?" is essentially a linear equation in slope-intercept form, y = mx + b.
First, find the slope. You got two points: (0, 70.7) and (6, 74.6). The x-coordinates are years since 1993, and the y-coordinates are the life expectancies.
$\displaystyle \begin{aligned}
m &= \frac{y_2 - y_1}{x_2 - x_1} \\
&= \frac{74.6 - 70.7}{6 - 0} \\
&= \frac{3.9}{6} \\
&= 0.65
\end{aligned}$
Second, you need the y-intercept. Oh, wait, one of the points is the y-intercept, so b = 70.7.
You have the two pieces of information needed to write the function:
E(t) = 0.65t + 70.7
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