In 1995​, the life expectancy of males in a certain country was 64.3 years. In 2001​, it was 66.9 years. Let E represent the life expectancy in year t and let t represent the number of years since 1995.
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Part 1
Find the linear equation that fits the data.
Eequals

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​(Round to the nearest tenth as​ needed.)

To find the linear equation that fits the given data, we first need to determine the slope and y-intercept of the line. The data provided gives us two points: 

- In 1995 (t = 0), the life expectancy (E) was 64.3 years.
- In 2001 (t = 6), the life expectancy (E) was 66.9 years.

Using these points, \((0, 64.3)\) and \((6, 66.9)\), we can find the slope \(m\) of the line with the formula:

\[
m = \frac{E_2 - E_1}{t_2 - t_1}
\]

where \((t_1, E_1) = (0, 64.3)\) and \((t_2, E_2) = (6, 66.9)\).

Substitute the values into the slope formula:

\[
m = \frac{66.9 - 64.3}{6 - 0} = \frac{2.6}{6} = 0.4333 \text{ (rounded to 0.4 to the nearest tenth)}
\]

Next, we use the point-slope form of the equation to find the y-intercept (\(b\)). The point-slope form is:

\[
E - E_1 = m(t - t_1)
\]

Using the point (0, 64.3):

\[
E - 64.3 = 0.4(t - 0)
\]

Simplify to find the equation of the line:

\[
E = 0.4t + 64.3
\]

So, the linear equation that fits the data is:

\[
E = 0.4t + 64.3
\]

Would you like more details or have any questions?

Here are 5 additional questions you might want to ask:

1. How do we interpret the slope in the context of this problem?
2. How can we use this linear equation to predict life expectancy in future years?
3. What other factors might affect life expectancy trends over time?
4. How do we determine the goodness of fit for this linear model?
5. How would the equation change if we used a different base year?

**Tip:** When finding the slope of a line using two points, always ensure the order of subtraction is consistent to avoid negative slopes when they are not applicable.

Discover how to find the linear equation that fits life expectancy data from 1995 to 2001. Step-by-step solution using the slope formula and point-slope form. Suitable for high school students learning about linear equations.

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