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Select the correct answer.

Lesle gathered the following data on the distance traveled and the cost of a ticket for a commuter train:

| Distance Traveled (miles) | 32 | 40 | 21 | 22 | 45 | 27 | 18 |
|----------------------------|-----|-----|-----|-----|-----|-----|-----|
| Ticket Cost (dollars) | 15.75 | 19.25 | 12.50 | 13.00 | 20.25 | 14.25 | 10.25 |

She used a scatter plot where [tex]\( x \)[/tex] represents the distance traveled and [tex]\( y \)[/tex] represents the ticket cost. The equation of the line of best fit is:

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

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

A. \[tex]$8.21
B. \$[/tex]4.81
C. \[tex]$354
D. \$[/tex]2.75



Answer :

GinnyAnswer
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].

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