Given the equation obtained from the line of best fit, [tex]\( y = 0.354x + 4.669 \)[/tex], where [tex]\(y\)[/tex] represents the cost of the ticket in dollars and [tex]\(x\)[/tex] represents the distance traveled in miles, we need to determine the cost to ride the train between two stations that are 10 miles apart.
Let's follow the steps:
1. Identify the distance traveled (x): In this case, [tex]\( x = 10 \)[/tex] miles.
2. Substitute [tex]\( x \)[/tex] into the equation: We substitute 10 into the equation [tex]\( y = 0.354x + 4.669 \)[/tex].
[tex]\[
y = 0.354 \cdot 10 + 4.669
\][/tex]
3. Calculate the value: Perform the multiplication and addition to find [tex]\( y \)[/tex].
[tex]\[
y = 3.54 + 4.669
\][/tex]
4. Simplify the result:
[tex]\[
y = 8.209
\][/tex]
So, the approximate cost to ride the train between two stations that are 10 miles apart is [tex]\( \$ 8.21 \)[/tex].
Therefore, the correct answer is [tex]\(\boxed{8.21}\)[/tex].
