Question
The scatter plot below shows the price of a movie ticket, in dollars, in the years since 1974. The line of best fit has the equation y=0.16x+1.52
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Which of the following is a true statement?
(1 point)
Responses
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $1.52 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $1.52 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $0.25 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $0.25 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to decrease by about $0.25 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to decrease by about $0.25 per year since 1974.
There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket.
There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket.
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.
Which of the following is a true statement?
(1 point)
Responses
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $1.52 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $1.52 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $0.25 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to increase by about $0.25 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to decrease by about $0.25 per year since 1974.
The slope of the line of best fit indicates that movie ticket prices tend to decrease by about $0.25 per year since 1974.
There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket.
There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket.
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Answers
GPT-4o mini
To analyze the equation of the line of best fit given by \( y = 0.16x + 1.52 \):
- In this equation, \( y \) represents the price of a movie ticket in dollars, and \( x \) represents the number of years since 1974.
- The slope of the line, which is \( 0.16 \), indicates that for each additional year since 1974, the price of a movie ticket tends to increase by $0.16.
Now, let's evaluate the statements provided:
1. "The slope of the line of best fit indicates that movie ticket prices tend to increase by about $1.52 per year since 1974."
- This statement is incorrect; the slope is 0.16, not 1.52.
2. "The slope of the line of best fit indicates that movie ticket prices tend to increase by about $0.25 per year since 1974."
- This statement is incorrect; the slope is 0.16, not 0.25.
3. "The slope of the line of best fit indicates that movie ticket prices tend to decrease by about $0.25 per year since 1974."
- This statement is incorrect; the slope is positive (0.16), indicating an increase, not a decrease.
4. "There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket."
- This statement is correct; the positive slope (0.16) indicates a positive association.
Therefore, the true statement is:
**There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket.**
- In this equation, \( y \) represents the price of a movie ticket in dollars, and \( x \) represents the number of years since 1974.
- The slope of the line, which is \( 0.16 \), indicates that for each additional year since 1974, the price of a movie ticket tends to increase by $0.16.
Now, let's evaluate the statements provided:
1. "The slope of the line of best fit indicates that movie ticket prices tend to increase by about $1.52 per year since 1974."
- This statement is incorrect; the slope is 0.16, not 1.52.
2. "The slope of the line of best fit indicates that movie ticket prices tend to increase by about $0.25 per year since 1974."
- This statement is incorrect; the slope is 0.16, not 0.25.
3. "The slope of the line of best fit indicates that movie ticket prices tend to decrease by about $0.25 per year since 1974."
- This statement is incorrect; the slope is positive (0.16), indicating an increase, not a decrease.
4. "There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket."
- This statement is correct; the positive slope (0.16) indicates a positive association.
Therefore, the true statement is:
**There is a positive association between the number of years that have passed between 1974 and the price of a movie ticket.**