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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=0.354 x+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]$\$[/tex] 8.21[tex]$

B. $[/tex]\[tex]$ 4.81$[/tex]

C. [tex]$\$[/tex] 3.54[tex]$

D. $[/tex]\[tex]$ 2.75$[/tex]

Sagot :

GinnyAnsweridn
To determine the approximate cost of a train ticket for a 10-mile trip based on the line of best fit provided, we will use the given linear equation:

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

Where [tex]\( y \)[/tex] represents the ticket cost in dollars and [tex]\( x \)[/tex] represents the distance traveled in miles. We need to calculate the ticket cost for [tex]\( x = 10 \)[/tex] miles.

Step-by-step solution:

1. Start with the given linear equation:
[tex]\[ y = 0.354x + 4.669 \][/tex]

2. Substitute the distance traveled ([tex]\( x = 10 \)[/tex]) into the equation:
[tex]\[ y = 0.354(10) + 4.669 \][/tex]

3. Perform the multiplication:
[tex]\[ y = 3.54 + 4.669 \][/tex]

4. Add the two numbers:
[tex]\[ y = 8.209 \][/tex]

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

[tex]\[ \$ 8.21 \][/tex]

Thus, the correct answer is:
A. \$ 8.21
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