Question
Up and Running Auto Shop keeps track of their regular customers' data to see if there is a relationship between the life of a car's engine, measured in number of miles driven (y)
), and the number of times the oil is changed (x)
). When the data is represented on a scatter plot, the equation for the line of best fit is y = 7,500x + 30,000
.
What is the meaning of the number 7,500
in the equation?
Responses
A For each additional oil change, the life of the car's engine is expected to increase by about 7,500
miles.For each additional oil change, the life of the car's engine is expected to increase by about 7 comma 500 miles.
B If the car has no oil changes, the car's engine is expected to last for about
miles.If the car has no oil changes, the car's engine is expected to last for about 7 comma 500 miles.
C Regardless of whether the car receives regular oil changes, the life of the car's engine is approximately
miles.Regardless of whether the car receives regular oil changes, the life of the car's engine is approximately 7 comma 500 miles.
D If the car has no oil changes, the life of the car's engine is expected to decrease by about
7,500 miles.
), and the number of times the oil is changed (x)
). When the data is represented on a scatter plot, the equation for the line of best fit is y = 7,500x + 30,000
.
What is the meaning of the number 7,500
in the equation?
Responses
A For each additional oil change, the life of the car's engine is expected to increase by about 7,500
miles.For each additional oil change, the life of the car's engine is expected to increase by about 7 comma 500 miles.
B If the car has no oil changes, the car's engine is expected to last for about
miles.If the car has no oil changes, the car's engine is expected to last for about 7 comma 500 miles.
C Regardless of whether the car receives regular oil changes, the life of the car's engine is approximately
miles.Regardless of whether the car receives regular oil changes, the life of the car's engine is approximately 7 comma 500 miles.
D If the car has no oil changes, the life of the car's engine is expected to decrease by about
7,500 miles.
Answers
GPT-4o mini
The correct interpretation of the number 7,500 in the equation \( y = 7,500x + 30,000 \) is:
**A**: For each additional oil change, the life of the car's engine is expected to increase by about 7,500 miles.
This is because the coefficient of \( x \) (which represents the number of oil changes) indicates how much the dependent variable \( y \) (the life of the car's engine in miles) increases for each additional unit of \( x \) (each additional oil change).
**A**: For each additional oil change, the life of the car's engine is expected to increase by about 7,500 miles.
This is because the coefficient of \( x \) (which represents the number of oil changes) indicates how much the dependent variable \( y \) (the life of the car's engine in miles) increases for each additional unit of \( x \) (each additional oil change).