The chart to the right shows a country's annual egg production. Model the data in the chart with a linear function, using the points $(0,52.7)$ and $(4,61.3)$. Let $x=0$ represent $1995, x=1$ represent 1996 , and so on, \begin{tabular}{|c|c|} \hline Year & $\begin{array}{c}\text { Egg production } \\ \text { (in billions) }\end{array}$ \\ \hline 1995 & 52.7 \\ \hline 1996 & 53.5 \\ \hline 1997 & 55.3 \\ \hline 1998 & 58.2 \\ \hline 1999 & 61.3 \\ \hline 2000 & 64.9 \\ \hline 2001 & 70.6 \\ \hline \end{tabular} to the actual data given in the table, 70.6 ?

Step 1 ：We are given two points (0,52.7) and (4,61.3) and asked to model the data with a linear function. The linear function can be represented as \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

Step 2 ：We calculate the slope using the formula \((y2 - y1) / (x2 - x1)\). Here, \((x1, y1) = (0, 52.7)\) and \((x2, y2) = (4, 61.3)\).

Step 3 ：The slope \(m\) is approximately 2.15.

Step 4 ：We substitute one of the points into the equation \(y = mx + c\) to find the y-intercept \(c\).

Step 5 ：The y-intercept \(c\) is 52.7.

Step 6 ：The linear function that models the data is \(y = 2.15x + 52.7\).

Step 7 ：To find the value of \(y\) when \(x = 6\) (which represents the year 2001), we substitute \(x = 6\) into the equation.

Step 8 ：The value of \(y\) is approximately 65.6.

Step 9 ：\(\boxed{\text{The linear function that models the data is } y = 2.15x + 52.7. \text{ When } x = 6 \text{ (which represents the year 2001), the value of } y \text{ is approximately 65.6. However, the actual data given in the table for the year 2001 is 70.6. Therefore, the linear function does not perfectly fit the actual data.}}\)