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Leslie gathered this data revealing the distance traveled and the cost of a ticket when taking a commuter train between six different pairs of stations.

\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
Distance Traveled (miles) & 32 & 40 & 21 & 22 & 45 & 27 & 18 \\
\hline
Ticket Cost (dollars) & 15.75 & 19.25 & 12.50 & 13.00 & 20.25 & 14.25 & 10.25 \\
\hline
\end{tabular}

She used a graphing tool to display the data in a scatter plot, where [tex]$x$[/tex] represents the distance traveled and [tex]$y$[/tex] represents the ticket cost. Then she used the tool to find the equation of the line of best fit:
[tex]y = 0.354x + 4.669[/tex]

Based on the line of best fit, what is the approximate cost to ride the train between two stations that are 10 miles apart?

A. [tex]\$8.21[/tex]
B. [tex]\$4.81[/tex]
C. [tex]\[tex]$3.54[/tex]
D. [tex]\$[/tex]2.75[/tex]

Sagot :

GinnyAnswer
To determine the approximate cost of riding the train between two stations that are 10 miles apart, we need to use the given line of best fit equation:
[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]$\$[/tex] 8.21$
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