## Answer :

[tex]\[ y = 0.354x + 4.669 \][/tex]

In this equation:

- [tex]\( y \)[/tex] represents the ticket cost in dollars,

- [tex]\( x \)[/tex] represents the distance traveled in miles.

Given that the distance [tex]\( x \)[/tex] is 10 miles, we will substitute [tex]\( x = 10 \)[/tex] into the equation to find the value of [tex]\( y \)[/tex], which represents the ticket cost:

[tex]\[ y = 0.354 \times 10 + 4.669 \][/tex]

Performing the multiplication and addition:

[tex]\[ y = 3.54 + 4.669 \][/tex]

[tex]\[ y = 8.209 \][/tex]

Thus, the approximate cost to ride the train for a distance of 10 miles is:

[tex]\[ \boxed{8.21} \][/tex]

Therefore, the correct answer is:

A. [tex]$\$[/tex] 8.21$