Question

the scatter plot and trend line describe the relationship between the average rent for a 1 - bedroom apartment in new york and the number of years after the year 2000. assuming the line correctly shows the trend in the data, what does it mean that the lines y - intercept is 800?
choose 1 answer:
a the average rent for a 1 - bedroom apartment in new york is approximately 800 dollars.
b on average, the rent of a 1 - bedroom apartment in new york increases by 800 dollars each year.
c the model indicates that 1 - bedroom apartments in new york had an average rent of approximately 800 dollars in 2010.
d the model indicates that 1 - bedroom apartments in new york had an average rent of approximately 800 dollars in 2000.

Explanation:

The x - axis represents the number of years after 2000. The y - intercept of a linear model \(y = mx + b\) (where \(b\) is the y - intercept) occurs when \(x = 0\). When \(x = 0\), it means 0 years after 2000, which is the year 2000. The y - value at \(x = 0\) (the y - intercept) represents the average rent when \(x = 0\) (in the year 2000).

• Option A is incorrect because it does not specify the year.
• Option B is incorrect as the y - intercept is not related to the rate of increase (the slope is related to the rate of increase).
• Option C is incorrect because 2010 is 10 years after 2000 (\(x = 10\)), not \(x = 0\).
• Option D is correct because when \(x = 0\) (0 years after 2000, i.e., 2000), the y - intercept of 800 means the average rent was approximately 800 dollars in 2000.

Answer:

D. The model indicates that 1 - bedroom apartments in New York had an average rent of approximately 800 dollars in 2000.