The scatter plot below shows how the number of posters sold each day at a museum is related to the cost per poster.
The museum manager drew the line of best fit on the scatter plot. Which statement best interprets the meaning of the y-intercept of the line of best fit?
A.
For each $1 increase in the price of the posters, about 1 fewer poster is sold.
B.
If the posters cost $40 each, the number sold is about 0.
C.
For each $1 increase in the price of the posters, about 1 more poster is sold.
D.
If the posters are free, about 40 posters are given away.
B. If the posters cost $40 each, the number sold is about 0.
B.
If the posters cost $40 each, the number sold is about 0.
To interpret the meaning of the y-intercept of the line of best fit, we need to understand what it represents. The y-intercept is the point where the line of best fit crosses the y-axis, which is the value of the dependent variable (number of posters sold) when the independent variable (cost per poster) is zero.
Looking at the given options:
A. This option states that for each $1 increase in the price of the posters, about 1 fewer poster is sold. However, this does not align with the y-intercept interpretation because it suggests that the number of posters sold could be negative when the cost per poster is zero.
B. This option suggests that if the posters cost $40 each, the number sold is about 0. This is consistent with the y-intercept interpretation because when the cost per poster is zero, there would be no posters sold.
C. This option states that for each $1 increase in the price of the posters, about 1 more poster is sold. Again, this does not align with the y-intercept interpretation because it suggests that the number of posters sold could be positive when the cost per poster is zero.
D. This option suggests that if the posters are free, about 40 posters are given away. This is consistent with the y-intercept interpretation because when the cost per poster is zero, there would be 40 posters given away.
Based on the above analysis, option D, "If the posters are free, about 40 posters are given away," is the statement that best interprets the meaning of the y-intercept of the line of best fit.