y = 4.75x + 5 represents the ticket price for a train based on distance traveled in miles. What prediction can be made based on the Line of Best Fit

Question

For $29, you can go 5 miles
It would cost $43 to travel 8 miles
You can pay less than $50 to travel 10 miles
You can pay just over $20 to go 3 miles

Answer 1

To analyze the predictions based on the equation \( y = 4.75x + 5 \), we can calculate the ticket prices for the given distances:

1. For 5 miles: \[ y = 4.75(5) + 5 = 23.75 + 5 = 28.75 \] This is less than $29, so the statement "For $29, you can go 5 miles" is True.

2. For 8 miles: \[ y = 4.75(8) + 5 = 38 + 5 = 43 \] The statement "It would cost $43 to travel 8 miles" is True.

3. For 10 miles: \[ y = 4.75(10) + 5 = 47.5 + 5 = 52.5 \] The statement "You can pay less than $50 to travel 10 miles" is False since it would cost $52.5.

4. For 3 miles: \[ y = 4.75(3) + 5 = 14.25 + 5 = 19.25 \] The statement "You can pay just over $20 to go 3 miles" is False since it would cost $19.25.

Summary of Predictions:

• True: You can go 5 miles for $29.
• True: It would cost $43 to travel 8 miles.
• False: You can pay less than $50 to travel 10 miles.
• False: You can pay just over $20 to go 3 miles.