Question

year (x).

\

$$\begin{tabular}{|c|c|} \\hline \\text{year born} & \\text{life expectancy (years)} \\\\ \\hline 1960 & 66.1 \\\\ \\hline 1970 & 67.6 \\\\ \\hline 1980 & 70.1 \\\\ \\hline 1990 & 71.9 \\\\ \\hline 2000 & 74.0 \\\\ \\hline 2010 & 75.9 \\\\ \\hline \\end{tabular}$$

which equation represents this linear model?

\\(y = 0.213x - 352.7\\)
\\(y = 0.213x - 358.4\\)
\\(y = 4.695x - 9181.6\\)
\\(y = 4.695x - 9322.4\\)

Explanation:

Calculate the average slope from the data points

$$
LATEXBLOCK0
$$

Comparing this with the given options, the slope must be approximately \(0.213\).

Solve for the y-intercept using a data point

Using the point \((1960, 66.1)\) and the slope \(m = 0.213\):

$$
LATEXBLOCK1
$$

Match with the closest option

$$
LATEXBLOCK2
$$

Answer:

• (A) \(y = 0.213x - 352.7\) (Correct answer)
• (B) \(y = 0.213x - 358.4\)
• (C) \(y = 4.695x - 9181.6\)
• (D) \(y = 4.695x - 9322.4\)